simultaneous compressive sensing and optical encryption … · simultaneous compressive sensing and...
TRANSCRIPT
SIMULTANEOUS COMPRESSIVE SENSING AND OPTICAL ENCRYPTION OF SIGNALS AND IMAGES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyScool of Electrical ampComputer Engineering Purdue UniversityIndiana USAersoypurdueedu andBogazici University Electrical and Electronic Engineering Department İstanbul Turkey
Assist Prof Dr Lale OumlzyılmazElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
Abstract
I Introduction
II Compressive Sensing Orthogonal Matching Pursuit
III Cryptography
IV Details of Implementation and Methods
V Experimental Results
VI Conclusions
References
CONTENTS
ABSTRACT
Compressive Sensing (CS) makes it possible to reduce the amount of data and thereby to greatly simplify the sensor system
In this method data is compressed before measurements whereas data is first measured and then compressed in the current technology
This approach leads to reducing the number of sensors
In this study simultaneous compressive sensing and optical cryptography is developed as a new approach for encryption and decryption of signals and images
ABSTRACT
CS is carried out with the Orthogonal Matching Pursuit (OMP) algorithm
The CS-OMP algorithm is next combined with the Double Random PhaseAmplitude Encyrption (DRPAE) method to achieve both compression and encyrption of data
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by the asymmetric RSA cryptography method
ABSTRACT
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encyrption method
In this approach data size is decreased and use of detection matrix in CS also protects DRPAE optical keys against well-known attacks
Experimental results both with 1-D signals and images are presented
I INTRODUCTION
According to classical signal processing methods when the signal is sampled Nyquist criteria must be satisfied to avoid loss of information
After sampling if the signal is compressible the signal is further compressed typically by a transform method
In the CS method the signal is supposed to be sparse in the sense that most signal values are assumed to be negligible(zero)
The signal is transformed by a measurement matrix to another space and measured in compressed form the measurement matrix must be such that the original signal can be recovered without loss
I INTRODUCTION
I INTRODUCTION
Several advantages of compression detection are given below
Reducing the number of sensors thereby transferring more information with fewer examples
Reducing the data loading process which is especially costly in image processing
Reduced power consumption and hardware complexity
I INTRODUCTION
Cryptography involves encryption and decryption of information
The mathematical methods for security of information data integrity and identity validation are significant topics of cryptography
In this study we propose a method for simultaneous compressive sensing encyrption and decryption of signals and images using orthogonal matching pursuit and optical cryptography
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
Abstract
I Introduction
II Compressive Sensing Orthogonal Matching Pursuit
III Cryptography
IV Details of Implementation and Methods
V Experimental Results
VI Conclusions
References
CONTENTS
ABSTRACT
Compressive Sensing (CS) makes it possible to reduce the amount of data and thereby to greatly simplify the sensor system
In this method data is compressed before measurements whereas data is first measured and then compressed in the current technology
This approach leads to reducing the number of sensors
In this study simultaneous compressive sensing and optical cryptography is developed as a new approach for encryption and decryption of signals and images
ABSTRACT
CS is carried out with the Orthogonal Matching Pursuit (OMP) algorithm
The CS-OMP algorithm is next combined with the Double Random PhaseAmplitude Encyrption (DRPAE) method to achieve both compression and encyrption of data
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by the asymmetric RSA cryptography method
ABSTRACT
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encyrption method
In this approach data size is decreased and use of detection matrix in CS also protects DRPAE optical keys against well-known attacks
Experimental results both with 1-D signals and images are presented
I INTRODUCTION
According to classical signal processing methods when the signal is sampled Nyquist criteria must be satisfied to avoid loss of information
After sampling if the signal is compressible the signal is further compressed typically by a transform method
In the CS method the signal is supposed to be sparse in the sense that most signal values are assumed to be negligible(zero)
The signal is transformed by a measurement matrix to another space and measured in compressed form the measurement matrix must be such that the original signal can be recovered without loss
I INTRODUCTION
I INTRODUCTION
Several advantages of compression detection are given below
Reducing the number of sensors thereby transferring more information with fewer examples
Reducing the data loading process which is especially costly in image processing
Reduced power consumption and hardware complexity
I INTRODUCTION
Cryptography involves encryption and decryption of information
The mathematical methods for security of information data integrity and identity validation are significant topics of cryptography
In this study we propose a method for simultaneous compressive sensing encyrption and decryption of signals and images using orthogonal matching pursuit and optical cryptography
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
ABSTRACT
Compressive Sensing (CS) makes it possible to reduce the amount of data and thereby to greatly simplify the sensor system
In this method data is compressed before measurements whereas data is first measured and then compressed in the current technology
This approach leads to reducing the number of sensors
In this study simultaneous compressive sensing and optical cryptography is developed as a new approach for encryption and decryption of signals and images
ABSTRACT
CS is carried out with the Orthogonal Matching Pursuit (OMP) algorithm
The CS-OMP algorithm is next combined with the Double Random PhaseAmplitude Encyrption (DRPAE) method to achieve both compression and encyrption of data
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by the asymmetric RSA cryptography method
ABSTRACT
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encyrption method
In this approach data size is decreased and use of detection matrix in CS also protects DRPAE optical keys against well-known attacks
Experimental results both with 1-D signals and images are presented
I INTRODUCTION
According to classical signal processing methods when the signal is sampled Nyquist criteria must be satisfied to avoid loss of information
After sampling if the signal is compressible the signal is further compressed typically by a transform method
In the CS method the signal is supposed to be sparse in the sense that most signal values are assumed to be negligible(zero)
The signal is transformed by a measurement matrix to another space and measured in compressed form the measurement matrix must be such that the original signal can be recovered without loss
I INTRODUCTION
I INTRODUCTION
Several advantages of compression detection are given below
Reducing the number of sensors thereby transferring more information with fewer examples
Reducing the data loading process which is especially costly in image processing
Reduced power consumption and hardware complexity
I INTRODUCTION
Cryptography involves encryption and decryption of information
The mathematical methods for security of information data integrity and identity validation are significant topics of cryptography
In this study we propose a method for simultaneous compressive sensing encyrption and decryption of signals and images using orthogonal matching pursuit and optical cryptography
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
ABSTRACT
CS is carried out with the Orthogonal Matching Pursuit (OMP) algorithm
The CS-OMP algorithm is next combined with the Double Random PhaseAmplitude Encyrption (DRPAE) method to achieve both compression and encyrption of data
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by the asymmetric RSA cryptography method
ABSTRACT
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encyrption method
In this approach data size is decreased and use of detection matrix in CS also protects DRPAE optical keys against well-known attacks
Experimental results both with 1-D signals and images are presented
I INTRODUCTION
According to classical signal processing methods when the signal is sampled Nyquist criteria must be satisfied to avoid loss of information
After sampling if the signal is compressible the signal is further compressed typically by a transform method
In the CS method the signal is supposed to be sparse in the sense that most signal values are assumed to be negligible(zero)
The signal is transformed by a measurement matrix to another space and measured in compressed form the measurement matrix must be such that the original signal can be recovered without loss
I INTRODUCTION
I INTRODUCTION
Several advantages of compression detection are given below
Reducing the number of sensors thereby transferring more information with fewer examples
Reducing the data loading process which is especially costly in image processing
Reduced power consumption and hardware complexity
I INTRODUCTION
Cryptography involves encryption and decryption of information
The mathematical methods for security of information data integrity and identity validation are significant topics of cryptography
In this study we propose a method for simultaneous compressive sensing encyrption and decryption of signals and images using orthogonal matching pursuit and optical cryptography
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
ABSTRACT
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encyrption method
In this approach data size is decreased and use of detection matrix in CS also protects DRPAE optical keys against well-known attacks
Experimental results both with 1-D signals and images are presented
I INTRODUCTION
According to classical signal processing methods when the signal is sampled Nyquist criteria must be satisfied to avoid loss of information
After sampling if the signal is compressible the signal is further compressed typically by a transform method
In the CS method the signal is supposed to be sparse in the sense that most signal values are assumed to be negligible(zero)
The signal is transformed by a measurement matrix to another space and measured in compressed form the measurement matrix must be such that the original signal can be recovered without loss
I INTRODUCTION
I INTRODUCTION
Several advantages of compression detection are given below
Reducing the number of sensors thereby transferring more information with fewer examples
Reducing the data loading process which is especially costly in image processing
Reduced power consumption and hardware complexity
I INTRODUCTION
Cryptography involves encryption and decryption of information
The mathematical methods for security of information data integrity and identity validation are significant topics of cryptography
In this study we propose a method for simultaneous compressive sensing encyrption and decryption of signals and images using orthogonal matching pursuit and optical cryptography
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
I INTRODUCTION
According to classical signal processing methods when the signal is sampled Nyquist criteria must be satisfied to avoid loss of information
After sampling if the signal is compressible the signal is further compressed typically by a transform method
In the CS method the signal is supposed to be sparse in the sense that most signal values are assumed to be negligible(zero)
The signal is transformed by a measurement matrix to another space and measured in compressed form the measurement matrix must be such that the original signal can be recovered without loss
I INTRODUCTION
I INTRODUCTION
Several advantages of compression detection are given below
Reducing the number of sensors thereby transferring more information with fewer examples
Reducing the data loading process which is especially costly in image processing
Reduced power consumption and hardware complexity
I INTRODUCTION
Cryptography involves encryption and decryption of information
The mathematical methods for security of information data integrity and identity validation are significant topics of cryptography
In this study we propose a method for simultaneous compressive sensing encyrption and decryption of signals and images using orthogonal matching pursuit and optical cryptography
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
I INTRODUCTION
I INTRODUCTION
Several advantages of compression detection are given below
Reducing the number of sensors thereby transferring more information with fewer examples
Reducing the data loading process which is especially costly in image processing
Reduced power consumption and hardware complexity
I INTRODUCTION
Cryptography involves encryption and decryption of information
The mathematical methods for security of information data integrity and identity validation are significant topics of cryptography
In this study we propose a method for simultaneous compressive sensing encyrption and decryption of signals and images using orthogonal matching pursuit and optical cryptography
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
I INTRODUCTION
Several advantages of compression detection are given below
Reducing the number of sensors thereby transferring more information with fewer examples
Reducing the data loading process which is especially costly in image processing
Reduced power consumption and hardware complexity
I INTRODUCTION
Cryptography involves encryption and decryption of information
The mathematical methods for security of information data integrity and identity validation are significant topics of cryptography
In this study we propose a method for simultaneous compressive sensing encyrption and decryption of signals and images using orthogonal matching pursuit and optical cryptography
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
I INTRODUCTION
Cryptography involves encryption and decryption of information
The mathematical methods for security of information data integrity and identity validation are significant topics of cryptography
In this study we propose a method for simultaneous compressive sensing encyrption and decryption of signals and images using orthogonal matching pursuit and optical cryptography
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the nonzero elements of a sparse signal from the measured signal
If the length m of the measurement vector is larger than k the number of nonzero elements of the sparse signal the sparse signal can be recovered by OMP with a very large probability
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
II COMPRESSIVE SENSING
ORTHOGONAL MATCHING PURSUIT
In the OMP program the detection matrix was generated by using one of a set of fast transforms namely Fast Fourier transform (FFT) Discrete Cosine Transform (DCT) Real Sinesoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T)
In the experiments discussed in Section 5 the ranking of transforms in terms of accuracy of results were DC3T DCT FFT RST DST Hadamard and Haar In addition DC3T has fewer number of multiplications than DCT
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
III CRYPTOGRAPHY
Cryptography refers to the methods of encryption and decryption of information
Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems
A cryptosystem involves five elements
P=PlaintextK=KeyE=EncryptionC=CiphertextD=Decryption
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
III CRYPTOGRAPHY
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
III CRYPTOGRAPHYSymmetric encryption algorithms use the same key for encryption and decryption operations
Symmetric encryption is very fast and easy to implement in electronic devices
In asymmetric encryption one general key is used for encryption and another special key is used for decryption
Asymmetric encryption algorithms are usually developed with very large prime numbers
In the proposed method the RSA algorithm was used for asymmetric encryption of the keys
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
III CRYPTOGRAPHY
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
RSA
III CRYPTOGRAPHY
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
III CRYPTOGRAPHY
Using asymmetric and symmetric encryptions together is named hybrid cryptography
Hybrid cryptography increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
IV DETAILS OF IMPLEMENTION AND
METHODS
Simultaneous Compressive Sensing and Hybrid Optical Cryptography (SCOSC) is proposed for effective and efficient compression and secure transmission of signals and images
In this work CS is achieved with the orthogonal matching pursuit (OMP) algorithm
Then the CS-OMP algorithm is combined with the double random phase plus amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
IV DETAILS OF IMPLEMENTION AND
METHODS
In order to achieve high security the keys used in CS and DRPAE are transmitted to the receiver by an asymmetric cryptography method (currently the RSA method)
Thus the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encryption method
In this approach data size is decreased and use of detection matrix in CS also improves DRPAE optical keys against attacks
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
IV DETAILS OF IMPLEMENTION AND
METHODS
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
IV DETAILS OF IMPLEMENTION AND
METHODS
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
Next the sparse signal per block is generated with length M satisfying MgeK log(N) by keeping M largest elements in magnitude and zeroing the others
The detection matrix is generated by pre and post multiplying a fast transform matrix with random permutation matrices
The SCOSC method is applied per block of information
IV DETAILS OF IMPLEMENTION AND
METHODS
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
The optical phaseamplitude keys p1 and p2 are generated with random complex numbers
The phase covers 360 degrees
This is repeated once more for a 4-f optical encryption system for additional security
The resulting encrypted signal with the overall system is of smaller size than the original signal
IV DETAILS OF IMPLEMENTION AND
METHODS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
V EXPERIMENTAL RESULTS
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
V EXPERIMENTAL RESULTS
Phase recovery and dirac delta function methods were studied for cryptoanalysis of the proposed method
Phase recovery methods are not effective when the keys of the 4f system are phaseamplitude keys
The dirac delta function method is effective in recovering the complete encryption matrix but this is not usable for decryption since OMP requires the measurement matrix which is not available
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
VI CONCLUSIONS
In this study a method for simultaneous compressive sensing using OMP and optical cryptography using double random phaseamplitude keys was proposed
The RSA algorithm involving asymmetric cryptography was used to encryptdecrypt the keys
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
VI CONSLUSIONS
The phaseamplitude keys were used in a 4f optical cryptography system
The measurement matrix for the OMP algorithm was also constructed using Fourier related fast transforms such as Discrete Fourier Transform (DFT) Discrete Cosine Transform (DCT) Real Sinusoidal Transform (RST) Haar wavelet transform Hadamard transform Discrete Sine Transform (DST) and Discrete Cosine-III Transform (DC3T) together with random permutation matrices
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
VI CONCLUSIONS
The experimental results with encryptiondecryption of 1-D audio signals and 2-D images showed that the method is capable of high accuracy encryption and decryption with correct keys
It was not possible to achieve correct decryption with 1-D and 2-D input signals when the keys were wrong
Cryptoanalysis studies with phase recovery and dirac delta function methods showed that the proposed method is extremely difficult to attack
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
[1] E J Candes ldquoCompressive samplingrdquo International Congress of Mathematicians (ICM) vol 3 pp 1433ndash1452 2006 Madrid Spain
[2] Mathematical Introduction to Compressive Sensing 2013 Simon Foucart Holger Rauhut Springer New York Heidelberg Dordrecht London ISBN 978-0-8176-4947-0
[3] httpusersecegatechedu_justinssp2007
[4] A Gilbert and P Indyk ldquoSparse recovery using sparse matricesrdquo Proceedings of the IEEE Vol 98 No 6 pp 937ndash947 2010
[5] Donoho D lsquolsquoCompressed Sensingrsquorsquo IEEE Tran Information Theory 52(4) pp 1289 -1306 April 2006
[6] C E Shannon ldquoCommunication in the Presence of Noiserdquo Proc Institute of Radio Engineers Vol 37 pp 10ndash21 1949
[7] httpinfonetgistackr
[8] Baraniuk R lsquolsquoCompressive sensingrsquorsquo IEEE Signal Processing Magazine 24(4) pp 118-121 July 2007
REFERENCES
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
[9] D Baron M B Wakin M F Duarte S Sarvotham and R G Baraniuk ldquoDistributed Compressed Sensingrdquo Tech Rep TREE-0612 Rice University Department of Electrical and Computer Engineering 2006
[10] Amir M A and Esther R lsquorsquo Compressive Sensing From Compressing while Sampling to Compressing and Securing while Sampling 32nd Annual International Conference of the IEEE EMBS Buenos Aires Argentina August 31 - September 4 2010
[11] Minal C and Rajankar S lsquorsquoStudy the Effects of Encryption on Compressive Sensed Datarsquorsquo International Journal of Engineering and Advanced Technology (IJEAT) ISSN 2249 ndash8958 Volume-2 Issue-5 June 2013
[12] Rachlin Y and Baron D ldquoThe Secrecy of Compressed Sensing Measurements Communication Control and Computingrdquo 2008 46th Annual Allerton Conference 813 ndash817 Urbana-Champaign IL
[13] C Dwork F McSherry and K Talwar ldquoThe Price of Privacy and the Limits of LP Decodingrdquo Symp on Theory of Computing (STOC) June 2007
REFERENCES
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
[14] Orsdemir A Altun HO Sharma G et al ldquoOn the Security and Robustness of Encryption via Compressed Sensingrdquo Proceedings of the IEEE military communications conference MILCOM 2008[15] Ramezani M Seyfe B Bafghi HG ldquoPerfect Secrecy via Compressed Sensingrdquo Communication and Information Theory (IWCIT) Iran Workshop on 8-9 May 2013 Tehran 1-5 2013
[16] Zhang Y Wong K Xiao D Zhang LY Li M ldquoEmbedding Cryptographic Features in Compressive Sensingrdquo Cryptography and Security Information TheoryarXiv14036213
[17] Zhang X Ren Y Feng G Qian Z ldquoCompressing Encrypted Image Using Compressive Sensingrdquo Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP) 2011 Seventh International Conference 222 ndash 225 Dalian 14-16 Oct 2011
[18] Yan Mo Aidi Zhang Fen Zheng Nanrun Zhou An Image Compression-Encryption Algorithm Based on 2-D Compressive Sensing Journal of Computational Information Systems 9 24 10057-10064 2013
[19] Donoho D Chen S and Saunders M ldquoAtomic Decomposition by Basis Pursuitrdquo SIAM Journal on Scientific Computing Vol 20 p33-61 1998
REFERENCES
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
[20] Tropp J and Gilbert AC ldquoSignal Recovery from Partial Information via Orthogonal Matching Pursuitrdquo IEEE Trans Inform Theory Vol 53 No 12 p 4655-4666 2007
[21] K Ersoy O and Nouira A lsquolsquoImage Coding With The Discrete Cosine-III Transformrsquorsquo IEEE Journal On Selected Areas In Communıcations Vol 10 No 5 June 1992
[22] B Schneier Applied Cryptography - Protocols Algorithms and Source code in C John Wiley amp Sons Inc 2nd edition 1996
[23]Washington L C 2003Elliptic Curves Number Theory and Cryptography ChapmanampHallCrc
[24] Menezes A J Handbook of Applied Cryptography Boca Raton CRC Press 1997
[25] Rivest R Shamir A ve Adleman L ldquo A Method for Obtaining Digital Signatures and Public-Key Cryptosystemsrdquo Communications of the ACM 21 (2)120-126 1978
REFERENCES
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr
Dr Ertan AtarTuumlrk Telekomİstanbul-I Area Officesİstanbul Turkeyertanatarturktelekomcomtr
Prof Dr Okan K ErsoyElectricampComputer Eng DeptPurdue UniversityIndiana USAersoypurdueedu Assist Prof Dr Lale Oumlzyılmaz
ElectronicsampCom Eng DeptYıldız Technical Universityİstanbul Turkeyozyilmazyildizedutr