a fast enhanced secure image chaotic cryptosystem based on hybrid chaotic magic...

Research ArticleA Fast Enhanced Secure Image Chaotic Cryptosystem Based onHybrid Chaotic Magic Transform

Srinivas Koppu1 and V Madhu Viswanatham2

1School of Information Technology and Engineering VIT University Tamil Nadu India2School of Computer Science and Engineering VIT University Tamil Nadu India

Correspondence should be addressed to V Madhu Viswanatham vmadhuviswanathamvitacin

Received 25 August 2016 Revised 26 October 2016 Accepted 20 November 2016 Published 4 January 2017

Academic Editor Aiguo Song

Copyright copy 2017 S Koppu and V M Viswanatham This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

An enhanced secure image chaotic cryptosystem has been proposed based on hybrid CMT-Lanczos algorithm We have achievedfast encryption and decryption along with privacy of images The pseudorandom generator has been used along with Lanczosalgorithm to generate root characteristics and eigenvectors Using hybrid CMT image pixels are shuffled to accomplish excellentrandomness Compared with existing methods the proposed method had more robustness to various attacks brute-force attackknown cipher plaintext chosen-plaintext security key space key sensitivity correlation analysis and information entropy anddifferential attacks Simulation results show that the proposed methods give better result in protecting images with low-timecomplexity

1 Introduction

With the rapid growth and application demand of multi-media data in open channels including Internet and wire-less networks in recent decades image security is one ofthe essential frameworks to provide the security for imagetransmission over the communication channels Multimediadata have become one of the most popular media types andare now used extensively in various fields such as politicseconomics defense and education Then because of datatransmission of open channels image transmission securityis subject to potential attacks Also exchange of medicalimage data has become a more important aspect of securityin recent decades For instance radiological and surgicalradios are more popular in the telemedicine Patient medicalreports are needed to be carried from one medical datastorage system to another for better treatment So if wedo not have privacy for data while transmission this maycause wrong diagnosis When we are sharing the patientinformation overwireless orwired communication networksthe security is more prominent General security servicesare confidentiality authentication and integrity [1] Thereare security fields available to provide security for image

such as image steganography watermarking cryptographyand hybrid algorithms Image encryption and decryptiontechniques based on public cryptographic and private cryp-tographicmethods are not optimized formedical image secu-rity due to intrinsic characters being time-consuming andrecovering image in the original image due to more pixelsreplication strong pixel relation between adjacent pixels andso forth DES AES RSA IDEA RC2 RC4 GOST andSAFEN may not good for encryption and decryption in fastcommunication applications because they may require morecomputational resources in the form of hardware and soft-wareDESAES and IDEAhad low-level efficiency in encryp-tion and decryption process However these algorithmsare more useful in text based encryption Telemedicinehad benefits restorative medical research remote specialclinical diagnosis unexpected incidents handling in timepatient information on immediate demand and enhancingthe communication between partners in health care systems

2 Literature Survey

The work by [2] employs a 3-dimensional cat map to shufflethe image pixels anduses the logisticmap to diffuse the image

HindawiModelling and Simulation in EngineeringVolume 2017 Article ID 7470204 12 pageshttpsdoiorg10115520177470204

2 Modelling and Simulation in Engineering

In this paper the authors addressed attacks such as statisticaland differential attacks Spatial permutation does not fit forpixel value modification in the image but it makes changesin pixel positions

Reference [3] applied a point-based interaction methodseffectively and feasibly to generate tangible textures fromstatic images and implemented a haptic virtual environmentbased on the OpenGL and PHANTOM Omni haptic devicefor the size of input image 128 times 128 However the proposedwork did not concentrate on security issues

The work by [4] explains a technique for image authenti-cation based on adding signal-dependent noise while takinginput image hidden noise was embedded into an image basedon film grain noise model Later original image and noiseare extracted for authentication purpose Here few attacksare addressed such as robust against content-preservingmodifications additive Gaussian noise local denoising anddetecting of malicious tampering Future work of this paperis to design an efficient noise filter for estimating the originalimage statistics

In [5] the authors presented a 2D image encryptionmethod based on balanced 2-Dimensional CellularAutomata(2DCA) Random image and original image are encrypted bypseudorandom number generator with a kernel value Theadvantages are as follows fast in encryption low-cost andlarge-size secret key Attacks addressed are such as statisticalanalysis correlation coefficients histogram analysis confu-sion analysis NPCR analysis and information entropy

In [6] a new image encryption has been proposed basedon chaotic Josephus matrix which extends the conventionalJosephus traversing method The future work of this papercan be applied to audio and video files for security purpose In[7] Lorenz Chaotic Scheme (LCS) and Chenrsquos hyperchaotic(CHC) method along with DNA sequences for an imageencryption algorithm that can dynamically select eight typesof DNA encryption rules and eight types of DNA additionand subtraction rules are used LCS was used to generatethe chaotic sequences to scramble the image CHC andDNA are used for image diffusion Here key size is 84 times10128 However authors have not addressed security issueshistogram analysis pixel correlation chart test and entropyIn [8] a new cross-layer unequal error protection (UEP) isintroduced which reduces image encryption overhead andcontrols the image bit stream structure to deliver the imagedata in wireless sensor networks This paper assures energycompetence and image security and quality over the imagetransmission in wireless network channels But the authorsdid not express their works on security issues such as brute-force attack key space analysis histogram analysis pixelcorrelation chaotic test and entropy

Reference [9] concentrates on open source EHRs alongwith parameters such as strengths weaknesses opportuni-ties threats of Electronic Health Record (EHR) over opensource EHRs and security services which are also notaddressed The work explained by [10] uses chaos mappingfunction to improve sensitivity of the initial state pixelposition changed by iterative function and XOR operationsfor diffusionThis paper combines chaos theory and iterativeequations based balanced pixel algorithm to decide the

number of iterations for the image encryption and resultantlow speed in image encryptionThe authors addressed in [11]tree proxy-based and service-oriented access control system(TPSACS) to fix secure detection of multimedia events inan online environment 1000 objects set as event block havebeen proposed to fix the scale robust illustration issue inonline services The future work can be applied in actionrecognition However security services are not addressed

Reference [12] proposed Tangent-Delay Ellipse ReflectingCavity-Map System (TD-ERC) wavelet neural networks(WNN) and XOR operations on binary data that achievescipher image Here addressed attacks are as follows keysize being 10195 histogram analysis correlation analysis anddifferential analysis The proposed system can be applied toprovide security for information Reference [13] introducedsymmetric chaotic economic map (CEM) with key space1084 the entropy that closes to ideal value 8 and low coef-ficient correlation that closes to 0 Initially CEM generateda chaotic sequence with fraction decimal values to integersAddressed attacks are key sensitivity analysis correlationanalysis and analysis of information entropy

In 2016 Kanso and Ghebleh [14] selected chaotic catmap algorithm used for medical image security applicationswith 119903 rounds and each round has two phases shuffling andmasking applied for block level as well as full image Themasking phase of each round uses a pseudorandom matrixof the same size as the input image to increase processingspeed Statistical cryptanalytic attacks such as key search anddifferential attacks are analyzed formedical image robustnessSame encryption and decryption technique are applied forROI as well as for full image and also achieved the same levelof security in ROI and full image Analyzed brute-force attackby considering key space is large However the author has notaddressed decrypted image quality and information entropy

In [15] 2-Dimensional Chaotic Map (2CDM) has beenconverted to 3-dimensional cat map (3DCM) for fast designand secure private image encryption with 128 bits Generallythe good cipher image will have less correlation amongpixels Here analyzed attacks are as follows statistical anddifferential attacks However brute-force and correlation ofimage attacks are not addressed This one is suitable for real-time Internet image security and telemedicine

In [16] a novel image encryption Using 3-dimensionalArnold cat map defends brute-force attack chosen-plaintextattack statistical attack and also image noise salt and peppernoise Gaussian noise and low-pass filter attacks Time takenfor encryption and decryption process for Lenna image (with256 times 256 sizes) was 0007 and 0012 seconds respectivelyBut chi-square test pixels correlation key space and entropyare not addressed

Reference [17] proposed pseudorandom permutationndashsubstitution method for image encryption based on loss-less symmetric block cipher The main design of proposedmethodwas to provide security for color image Computationspeed of encryption process has been increased by directlyshuffling row by row and column by column instead of pixelby pixel Security parameters are considered in the proposedmethod the histograms correlation coefficients informationentropy key sensitivity analysis differential analysis and key

Modelling and Simulation in Engineering 3

space analysis Further this method can be used in videoencryption and grayscale images

In [18] chaos based image encryption by using streamcipher and pseudorandom generator is based on cascade ofchaotic maps DES AES RSA and IDEA may not be goodfor encryption in fast communication applications becausethey may require more computational resources in the formof hardware and software In this method initially inputimage converts into binary bit stream and is masked withpseudorandom key generator then encryption image wasconstructed For fast pseudorandom key generator finiteprecision exemplification and fixed point arithmetic areespoused Resisted statistical attacks color histogram forRGB Lenna image correlation of adjacent pixels in verticalhorizontal and diagonal directions and brute-force attackare addressed by taking 192-bit key

In [19] Region of Interest (ROI) is used as water markingand encrypted by linear feed backshift register using streamcipher mode with 64-bit private and public key embeddedintomedical image by spread spectrummethod Second-timeencryption had been done by Diffie-Hellman algorithm Inthis paper the authors have used medical images modalitiesMRI CT-scan and X-ray However these approaches have adrawback as they could not recover original medical image

In [20] high security visual encryption algorithms hadbeen proposed with two-level encryption strategies in firstlevel image pixels had been shuffled with row-wise andcolumn-wise permutation based on tent map so that it affectsvisual perception In second level diffusion was applied forshuffled image with 4D hyperchaotic Chen systems Pixelcorrelation was truncated and procured privacy for patientimage with tent maps Hyperchaotic security system haddynamic features compared with other conventional chaoticmethods Image security measurements considered are asfollows statistical analysis chi-square test pixels correlationkey space and entropy In this paper authors used inputimage modalities MRI images with 568 times 568 CT-scanabdomen image with 512 times 512 and X-ray angiography with1024 times 1024 sizes for experiments and they suffered from lowspeed process

In [21] DICOM image format is used to achieve secu-rity over Internet transmission DICOM has two attributesheader attribute and pixel dataWith help of digital signatureauthenticity and integrity had been obtained on pixel datafor basic level However confidentiality of the pixel datahas not been addressed in confidentiality profile in DICOMAdvanced Encryption Standard-Galois Counter Mode (AES-GCM) the Whirlpool hash function and the Elliptic CurveDigital Signature Algorithm provide confidentiality authen-ticity and integrity for header and pixel values of DICOMWith lack of confidentiality sometimes plain image willget interfered condensed and edited With lack of digitalsignature anyone may edit an image by using tools whichmay lead to improper result in diagnostic process for medicalexperts Limitations in [21] are addressed by Kobayashi etal [22] scheme Data pixel confidentiality is achieved byusing encryption standard in DICOM header However keysare stored in DICOM header without encryption so it maynot give confidentiality assurance Kobayashi et al scheme

does not provide confidentiality authenticity and integrityfor the DICOM header data However this approach takesmore time for encryption and decryption on large-size IVUSimages

In [23] authenticity and integrity (AIDM) had fourmodules preprocessingmodule image hashingmodule dataencryption and data embedding RSAREF free tool kit wasused for data encryption Future work of the proposedalgorithm is to improve the speed in encryption-decryptionprocess and key management Digital signature and MD5are used for verification authenticity and integrity [24] Sym-metric encryption algorithms are used for electronic patientrecords (EPR) Bipolar TER Multiple Base was developedwhich provides basic security services integrity authentica-tion and confidentiality Time complexity is O (N) Howeverthe proposed approach is suffering from lack of security

In [25] AES-GCM is faster than conventional methodssuch as AES CBC + HMAC-SHA1 AES CBC + HMAC-SHA256 and RC4-SHA1 Whirlpool hash function is morepowerful than MD5 SHA-1 SHA-224 SHA-256 and SHA-384 SHA-512 andWhirlpool had the same strengths in secu-rity [1] Matrix Array symmetric-Key Encryption (MASK)was applied for image encryption based on a private keyand it is faster than AES algorithm 128 bits are used as keysize and image block size But key size is less and leads tobrute-force attack In [26] McEliece public cryptosystemsand Sequitur compression technique are used for medicalimages yielding better efficiency than RSA cryptosystemsAuthenticated image encryptionwas achievedwithout digitalsignature McEliece public cryptosystem has better adeptnessand security thanRSA algorithmHowever the usedmethodsdid not analyze statistical and differential attacks brute-forceand correlation

Image is encrypted with secret key and secret keyencrypted with public key technique [27] The major issueis key distribution at the same time we have to transferencrypted image and encrypted key over a network In thispaper hybrid method is proposed based on cryptosystemsand DCT water marking method The image encryption hasbeen done with either stream or block cipher Sometimesblock cipher is not feasible due to lack of robustness andhomogenous regions Stream ciphers are robust to adequateJPEG compression noise Stream cipher examples are RC4one-time pad or Vernam cipher and so forth Result obtainedwith PSNR is 4371 dB

In [28] used digital envelope (DE) digital signatureand encrypted patient information from DICOM headerare embedded as invisible water mark in image for authen-tication confidentiality integrity in atmosphere of picturearchiving and communication systems (PACS) DE process-ing has taken more time to be embedded in image andDE is very expensive because of stream cipher encryptionHowever thismethod did not concentrate onDICOMheadersecurity Reference [29] proposed new 2D-sine logistic mod-ulation maps (2D-SLMM) based on logistic and sine mapswith efficient image pixel shuffling algorithm known asChaotic Magic Transform (CMT) to derive random pixelproperty encryption image In digital images usually highredundancy data will be there due to high correlation of


pixels to break these correlations CMT used CMT changespixels values in random position 2D chaotic maps have goodperformance in terms of generating chaotic sequence than1D chaotic map but they need relatively complex hardwarestructure and cost CMT performance is better at shufflingthan early chaotic maps Chaotic performance is analyzedby the following parameters trajectory Lyapunov exponentand Lyapunov dimension andKolmogorov entropy survivingchaotic maps are broadly classified into 1D chaotic mapsand high-dimensional maps 1D map has one variable andfew attributes with simple design structure for examplelogistic sine Gaussian and tent maps CMT-IEA is basedon asymmetric cryptosystems HD chaotic maps shall haveminimum of two attributes with complex structure whichgives more chaotic enactment for example Henon mapLorenz map systems and Chee-Lee systems

Reference [30] used chaotic schema with linear congru-ence based on pseudorandom numbers generation that iscoupling of chaotic function with XOR operations duringencryption process to achieve randomness in cipher imageand large key space to resist brute-force attack If the imagehas high correlation with adjacent pixel values they need toincrease the quality of cipher image during encryption anddecryption process In order to address the high correlationproblem we need to mix and change the values of pixelssimultaneously However authors did not concentrate onfloating point values while doing encryption and decryptionprocess

In [31] chaos based cryptosystem was proposed in 1989Chaos properties are as follows sensitive dependence initialconditions and system parameters pseudorandom propertynonperiodicity and topological transitivity In this systemplan image is shuffled by logistic 1D map and encryptedwith hyperchaotic systems which is based on Chenrsquos chaoticsystem Brute-force attack was considered But this papersuffers from statistical attack histogram metric entropy andchi-square test Most of the chaos based security techniquessuffered from chosen-plaintext attack [32] Based on three1D chaotic methods logistic tent and sine map utilizingthe same arrangement of security keys the proposed methodhas the capacity to produce a totally diverse encrypted imageevery time when it is applied to the original image

In [33] new parametric switching chaotic system usingsine map and tent map is controlled by logistic map Theoutput of the logistic map decides to choose either the sinemap or the tentmap as a generator to deliver PSCSrsquos output bitsequence Some attacks addressed are as follows brute-forceattack security key space key sensitivity correlation analysisand information entropy differential attacks Gaussian noisesalt and pepper noise and so forth However chosen-plaintext and cipher plaintext were not addressed

In [34] C-J Cheng and C-B Cheng proposed asym-metric image encryption method based on unified chaoticsystem Lyapunov stability theory and a cellular neuralnetwork-adaptive controller with its parameter update lawIn this paper the authors considered key space analysis asensitivity test and statistical analysis In [33 34] chosen-plaintext and cipher plaintext were not addressed Howeversimulations results are not shown in real-time applications

In [35] chaotic map lattices (CML) had weakness con-versation of floating values into pixel valuewhich leads to dataloss in image Improved CML was proposed by Jasteazebskiand Kotulski based on CBC method but lacks from varioussecurity services such as noise attacks differential attacks andstatistical attacks Image encryption conceals some particularissues for example huge size of image pixels and redundancyIn some cases the value of pixel in encryption process willdepend on the neighboured pixel value that is pixels blocksHowever the key size is small which may give brute-forceattack In this paper the authors considered time complexityspace complexity noise attacks differential attacks statisticalattacks and so forth In medical image encryption has beendeveloped based on modular arithmetic operator [36] In[37] the proposed technique has four differential chaoticsystems yielding image confusion In [38] chaos basedimage encryption has been applied for bit planes basedon pseudorandom binary number generator The authorsaddressed speed and time issues However it lacks varioussecurity services such as noise attacks differential attacks andstatistical attacks

Bakermap has been proposed [39] to represent real num-ber while doing encryption and decryption process Blocklevel image encryption based on self-invertible matrices withtwo mere different keys [40] Color images are divided intothe three subband array of images red green and blue arejumbled by Fibonacci Transformation (FT) and encryptedwith hybrid cellular automata [41] Medical image securityis using Game of Life (GoL) and DNA sequence in DWTand spatial domain [42] However noise attacks chosen-plaintext attacks differential attacks and statistical attacks arenot addressed

21 Review Nowadays most of the researchers have pro-posed a cryptographic system based on spatial and frequencydomain image encryption methods which are not suitablefor efficient image encryption Chaotic research for an imageencryption has a vital significance due to sensitive depen-dencies on initial conditions system parameters randombehavior nonperiodic and topological transitivity and soforth chaotic systems are used for image encryption thatcannot be recognized by malicious users Even if the attackeris intercepted the image will not be identified so that itcan transfer successfully over the Internet which guaranteesthe security of image communication Most of the papershave not addressed security services such as pixel correlationchosen-plaintext attack cipher attack histogram analysisand entropy [24ndash28]The proposedmethods are described inSections 3 and 4 alongwith experimental results In Section 3we have described hybrid CMT (HCMT) which gives morerobustness for protecting the images from various attackslike key space analysis key sensitivity pixel correlationhistogram analysis chosen-plaintext attack cipher attackentropy and noise analysis

3 Proposed Method

The main idea to encrypt a plain image is to permutate thepositions of pixels and to conceal the values of pixels via


1 3 4 1

4 2 2 2

3 1 1 4

2 4 3 3

23 8 48 10

37 17 83 54

199 66 101 93

247 71 107 252

23 66 107 10

247 17 83 54

199 8 48 252

37 71 101 93

Column Sorting

C C998400 I

Figure 1 Generation of index matrix 119868

I PM

1 3 4 1

4 2 2 2

3 1 1 4

2 4 3 3

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

10 3 4 15 8 13 6

2 15 11 12

7 14 4 9

I Pixel shuffling

Figure 2 Pixel shuffling process

different methods commonly The two-dimensional featureof the image is employed in our encryption scheme com-pared with traditional encryption schemes HCMT-EE is alightweight image encryption method based on hybrid CMTwith Lanczos algorithm This shows better experimentalresults than [2 6 28 42]This paper presents Hybrid ChaoticMagic Transform (HCMT) liner congruential generator(LCG) and Lanczos algorithm to build a fast enhanced secureimage chaotic cryptosystem Input plain image 119875 is givento the HCMT as shown in Figure 3 HCMT has four stepsimage column pixel values are sorted in ascending orderand performed a row sorting Pixel confusion phase achievesconfusion property by randomly shuffling all pixel positionsobtaining confused image119872

The pseudorandom generator has used to generate key(119870) with a size of host image 119875 This key (119870) is given to theLanczos algorithm to find the vector characteristics whichimprove the key space and enhance security against thepotential attacks Cipher image (119885) is obtained by performingthe multiplication operation between key vectors (119870) andconfused image (119872)

31 Hybrid Chaotic Magic Transform The aim of adaptedencryption algorithm is to confuse the position of pixels foreach block of the image based on the following steps

Hybrid CMT (ChaoticMagic Transform) algorithm shuf-fles matrix 119862 [29]

(1) Sort each column of 119862 in ascending order to obtainsorted matrix 1198621015840

(2) Generate shuffled index matrix 119868 by connectingthe pixels in 119862 with locations (119897(119894 1) 1) (119897(119894 2) 2)(119897(119894 3) 3) (119897(119894 4) 4) (119897(119894 119899) 119899)with respect to CO

(3) The pixel shuffling process is done by shuffling thepixels 119875 positions to the right in the clockwisedirections

HCMT used the right direction in the clockwisedirections which enables shuffling image pixelsquickly in both the row and column directions at thesame time Experimental results and security analysisshow that the proposedHCMT-EE can encrypt differ-ent types of digital images with a high level of securitywith low-time complexity Image pixel shifting hasfour steps in the first iteration we have shifted onlyone pixel position to the right In the second iterationwe have shifted to two pixel positions in the rightdirection In the third iteration three pixel positionsare shifted In the fourth iteration four pixel positionsare shiftedThe clockwise direction pixel shifting gavemore image randomness than left clockwise shiftingmethod with fast encryption speed

(4) The resultant shuffled matrix is119872The shuffling process is done by using the hybrid CMTalgorithm here random chaotic matrix 119862 with size 119898 times 119899 isused to produce the shuffled index matrix 1198621015840 of size 119898 times 119899where index matrix 119868 is defined by

119868 (119894 119895) = 119896 for 1198621015840 (119894 119895) = 119862 (119896 119895) (1)

Let 119874 be the original image with size 119898 times 119899 and 119872 be theresultant shuffled image The pixel shuffling process of theoriginal image is defined by

119865 (119875 119868) = 119872 (2)

Figures 1 and 2 are the example of CMT process Figure 1shows the generation of shuffled indexed matrix 119868 fromchaotic matrix 119862 As shown in Figure 1 sorted matrix 1198621015840is generated by sorting each column of chaotic matrix 119862 inascending orderThe index matrix shows the position of data1198621015840 where they are permuted from chaotic matrix 119862 Figure 2shows the pixel shuffling processwhere119875 is the original imagematrix and119872 is the resultant shuffled matrix obtained fromHCMT


Column sorting

HCMT

GEM shuffling

Row sorting

Pixel confusion

Key matrix K

Lanczos algorithm

Calculate vector

characteristics

Start

End

Host image P

Pseudorandomkey generator

Cipher image ZConfused image M

Z = Mlowast K

Figure 3 Proposed framework for image encryption

32 Pseudorandom Generator A linear congruential genera-tor (LCG) is used to generate119898times 119899 pseudorandom numbersby using

119883119899+1 = (119886119883119899 + 119887)mod119898 (3)where 119886 and 119887 are integers and119898 is the start value

33 Lanczos Algorithm [43] The application of Lanczosalgorithm is to perform normalization on large eigenvaluesand eigenvectors It was invented by Cornelius Lanczos [43]We used 1199021 as the random vector matrix ldquo119896rdquo 119882119898 is thecharacteristic roots and 120572119898 is the characteristic vectors forloops being used to calculate eigenvalues and eigenvectorsLanczos algorithm is as follows

StartInitialization1199021 = random vector with norm 11199020 = 01205731 = 0

Step 1for 119894 = 1 2 3 119898 minus 1

Step 1-1 1199081119894 larr 119896119902119894Step 1-2 120572119894 larr 1199081119894 sdot 119902119894Step 1-3 119908119894 larr 1199081119894 minus 120572119894119902119894 minus 120573119894119902119894minus1


25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(a)

25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(b)

500

400

300

200

100

0

0 50 100 150 200 250

0 50 100 150 200 250

600

500

400

300

200

100

0

(c)

0 50 100 150 200 250

1200

1000

800

600

400

200

0

0 50 100 150 200 250

600

500

400

300

200

100

0

(d)

0 50 100 150 200 250

4000

3500

3000

2500

2000

1500

1000

500

0

Red componentGreen componentBlue component

0 50 100 150 200 250

2500

2000

1500

1000

500

0


Red componentGreen componenBlue component

(e)

Figure 4 This figure shows simulation results of various images with their histograms (a) all-zero pixel image (b) all-one pixel image (c)image with text (d) medical image (e) color image

Step 1-4 120573119894+1 larr 119908119894Step 1-5 119902119894+1 larr 119908119894120573119894+1

End forStep 2 119902119898 larr 119896119902119898Step 3 119860119898 larr 119908119898 sdot 119902119898Return

4 Simulation Results Analysis

The proposed method HCMT-EE has ephemeral encryptionand decryption process for the USC-SPI ldquoMiscellaneousrdquodataset The experimental results are performed using MAT-LAB R2015a on a personal computer with a Intel corei5-4200U CPU 160GHz 8GB memory and 500GB hard-disk capacity and Microsoft Windows 81 64-bit operatingsystem Our simulation results are shown in Figures 4

and 5 Figures 4(a)ndash4(e) show histogram simulation resultsfor image with all-zeros all-ones image image with textmedical image and color image HCMT-EE shows enhancedperformance for image encryption by transforming arbitraryand homogeneous distribution to the entire image into cipherimage or unpredictable form Figures 5(a)ndash5(h) show the keyspace analysis (a) Input plain image (119875) (b) encrypted image1198641 = Enc(1198751198701) (c) encrypted image 1198642 = Enc(1198751198702) (d)difference of encrypted image 1198641 minus 1198642 (e) decrypted image1198631 = Dec(1198641 1198701) (f) decrypted image 1198632 = Dec(1198641 1198702)(g) decrypted image 1198633 = Dec(1198641 1198703) (h) difference ofdecrypted image 1198642 minus 1198643

41 Time Complexity HCMT-EE method has high speedencryption results compared to [29 44ndash47] All input imagesare tested using MATLAB from the USC-SIPI ldquoMiscella-neousrdquo dataset which is not randomdataset Table 1 shows the


(a) (b) (c) (d)

(e) (f) (g) (h)

Figure 5 Key space analysis (a) input plain image (119875) (b) encrypted image 1198641 = Enc(119875 1198701) (c) encrypted image 1198642 = Enc(119875 1198702) (d)difference of encrypted image 1198641 minus 1198642 (e) decrypted image 1198631 = Dec(1198641 1198701) (f) decrypted image 1198632 = Dec(1198641 1198702) (g) decrypted image1198633 = Dec(1198641 1198703) (h) difference of decrypted image 1198642 minus 1198643

Table 1 Encryption speed (seconds) of various encryption algo-rithms

Image size 64 times 64 128 times 128 256 times 256 512 times 512 1024 times 1024Wu et alrsquos [47] 02503 13412 56544 271702 1099320Zhou et alrsquos [32] 00174 00549 01967 06547 32415Wu et alrsquos [46] 00161 00582 02368 08587 35037Liao et alrsquos [45] 00546 01415 05630 22597 90046CMT-IEA [17] 00042 00130 00538 02338 11494HCMT-EE 00042 00129 00542 01814 09144

comparison of various encryption and decryption algorithmsalong with their input image sizes ranging from 64 times64 to 1024 times 1024 and observed HCMT-EE has the highencryptiondecryption speed The speed of the encryptionprocess was improved for images with a large-size 512 times 512and 1024 times 1024 is 01814 and 09144 respectively HenceHCMT-EE had less time complexity for large-size images

Table 1 shows a comparison of [29 44ndash47] enhancedexperimental encryptiondecryption speed results tested onseveral input images using MATLAB

42 Histogram Analysis The histogram is used to showthe number of pixels per gray level The histograms of theencrypted images are plotted in Figure 4 It shows that thehistogram of the cipher image is uniform which defendsagainst statistical attack In Figure 4 the first row shows alloriginal images which include grayscale images and colorimages The second row shows histogram of the originalimages The third row shows encrypted images of original

imagesThe fourth row gives a histogramof encrypted imagesthat are very relatively uniform

43 Pixel Correlation In digital images usually high redun-dancy data will be there thus giving high correlation amongthe neighbour pixels A good cryptosystem can reduce thecorrelation between pixels which resist statistical attack Datacorrelation is defined in [29]

119862119903119903 =119864 (119883 minus 120583119883) (119884 minus 120583119884)

120590119883120590119884 (4)

where119862119903119903 is the correlation119883 and119884 are datasets and 120583 is themean value in the standard deviation If119883 and 119884 have a highcorrelation their119862119903119903 value is close to 1 Otherwise it is close 0To analyze and compare the correlation of the adjacent pixelsin the plain and cipher image 2500 random pair pixels arechosen in each direction from plain image and cipher imageThe correlation of two adjacent pixels in three directions isshown in Table 2 Equation (4) is used to calculate correlationamong two adjacent pixels which gives better results than [1529]

44 Entropy Entropy gives uncertainty present in the cipherimage If the entropy of the cipher image is high image hashigh randomness and high confidentiality [29]

119867(119896) = minus119899

sum119894=1

119875119903 (119896119894) log2119875119903 (119896119894) (5)

where 119896 is the collection of pixels 119896119894 119894th is possible value in119896 119875(119896119894) is the probability of 119896119894 Input images 5109sim7201 are


Table 2 This table shows pixel correlation of Lenna image withCMT 3D chaotic map algorithm and HCMT-EE

Method Images Horizontal Vertical Diagonal

CMT [29]

Originalimage 09659 09366 09153

Cipherimage 00023 minus00085 00402

3D chaoticmap [15]

Originalimage 091765 095415 090205

Cipherimage 001183 000016 001480

HCMT-EE


Cipherimage minus00049 minus00638 minus00012

tested using MATLAB from the USC-SIPI ldquoMiscellaneousrdquodataset The results are listed in Table 3 It is obvious that theentropies of the cipher images are close to the ideal value 8which means that the probability of accidental informationleakage is very small

45 Peak Signal Noise Ratio Peak Signal Noise Ratio mea-sures the similarity between original image and receivedimage If the PSNR value is high the correlation betweenoriginal image and received image is high

PSNR = 10 lowast log102552

MSEdB (6)

46 MSE (Mean Square Error) In this method the qualityof the image is calculated by averaging the squared intensityvalues of difference of modified image and host image

MSE = 1119872119873

119872minus1

sum119909=0

119873minus1

sum119910=0

(119891 (119909 119910) minus 1198911015840 (119909 119910))2 (7)

where119872 times 119873 is the size of the image 119891(119909 119910) is the originalimage value at (119909 119910) pixel and 1198911015840 is the decrypted imagevalues at (119909 119910) pixel

47 Key Space Analysis The strength of the key dependson the size of the key which is used for encryption anddecryption of the image In proposed method we considerthat the key size is 256 bits and thus key space is 2256 Thisis sufficiently substantial to oppose brute-force attack Inencryption process we have used two sensitive encryptionkeys yielding totally different cipher image In part of decryp-tion process we have two sensitive decryption keys to recoverencrypted image and the recovered images are completelydissimilar Figure 5 shows that using1198701 key derived two keys1198702 and 1198703 with one-bit difference to encrypt plain imageinto random image input plain image (a) is encrypted using1198701 amp 1198702 and results in (b) and (c) are completely different asshown in (d) Encrypted image (b) completely is decryptedas shown in (e) Cipher images are decrypted in (f) and (g)

with two keys of one-bit difference from 1198701 being totallydifferent Hence the proposed system is excellent in keysensitive process of encryption and decryption

48 Noise Analysis During the public transmission of imageover the Internet or devices the noise may attack imagesthat may degrade the quality of the image salt and pepperGaussian and low-pass filter attack are general noise attacks[3]

In the proposed method while shuffling the pixels tovarious positions in the image image value positions can bechanged automatically it makes chosen-plaintext infeasibleIn proposed strategy while rearranging the pixels to differentpositions in the image naturally image qualities can bechanged it makes chosen-plain text unfeasible

5 Conclusion

This paper proposed HCMT-EE which shows excellentsimulation results for time complexity key space analysisvarious noise attacks pixel correlation and so forth we haveobserved the performance of HCMT-EE in image securityapplications Lanczos algorithm has been used to find eigen-vector and eigenvalues in low-time complexity GEM shiftinghas been used for image pixel shiftingThe proposed HCMT-EE may apply in rain image recovery applications and 3D-medical image security

Abbreviations

AES Advanced encryption standardAIDM Authenticity and integrity for

mammographyCBC Cipher block chainingCML Chaotic map latticesCMT Chaotic Magic TransformCT-scan Computerized tomography scanDCT Discrete cosine transformDES Data encryption standardDICOM Digital imaging and communications in

medicineDSA Digital Signature AlgorithmDWT Discrete wavelet transformEPR Electronic patient recordsFT Fourier transformGCM Galois Counter ModeGoL Game of LifeHMAC Hashed message authentication codeIDEA International data encryption algorithmIVUS Intravascular ultrasoundMASK Matrix Array symmetric-Key EncryptionMD5 Message Digest-128 bitsMRI Magnetic resonance imagingPACS Picture archiving and communication

systemPSNR Peak Signal to Noise RatioRC2 Rivest Cipher 2


Table 3 This table shows pixel correlation of the line image with CMT 3D chaotic map algorithm and HCMT-EE

File name Wu et alrsquos [46] Zhou et alrsquos [33] Liao et alrsquos [45] Zhang et alrsquos [44] CMT-IEA [29] HCMT-EE5109 7901985 7903354 7903764 7904191 7902127 79022275110 7902731 7902443 7901801 7902731 7903402 79032015111 7902446 7902756 7903306 7900799 7902687 79024785112 7902556 7901526 7904478 7903374 7901906 79017525113 7902688 7904563 7904657 7904566 7902825 79026135114 7903474 7902954 7902874 7903111 790234 79023245208 7903953 7902356 7903218 7901762 7903327 79031105209 7902233 7899853 7903089 7905854 7901765 79016735210 7900714 7902654 7902077 7902768 7902748 79026145301 7902727 7902647 7902108 790104 7901772 79014525302 7903182 7910474 7904169 7903328 7900981 79008477101 7902173 7902634 7901965 7902145 7901305 79012057102 7900879 7901634 790497 7902157 7901578 79013377103 7902543 7905423 7891503 7900645 7903099 79029307104 7901126 7902125 7903399 7904141 7902607 79021357105 7903579 7883653 7901301 7900027 7905305 79042037106 790193 7902356 7903367 7901736 7902695 79024257107 7903000 7902364 7899556 7900802 7902896 79024237108 7903197 7904456 7883531 7900944 7901632 79016347109 7902308 7903012 7903201 7905658 7903173 79026537110 7899542 7901598 7901542 7893848 7901524 79014107201 7902772 7901989 7904945 7904525 7902454 7902104boat512 7901908 7901879 7903091 7900712 7903088 7902745elaine512 7901122 7902989 7901859 790203 790172 7901679gray21512 790017 7905107 7901832 7902149 7902688 7902677numbers512 7903615 7892351 7902144 7903579 7901657 7901437ruler512 7903265 7903001 7901937 7901428 7903052 7903045testpat1k 7902806 7901681 7903856 7903343 7902752 7902378Mean 7902308 7901923 7903764 7902167 7902488 7902169Pass rate 1828 2028 1728 1128 2628 2628

ROI Region of InterestRSA Rivest-Shamir-Adleman algorithmSHA-1 Secure Hashing Algorithm

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] A J Paul P Mythili and K Paulose Jacob ldquoMatrix basedcryptographic procedure for efficient image encryptionrdquo inProceedings of the IEEE Recent Advances in Intelligent Compu-tational Systems (RAICS rsquo11) pp 173ndash177 Trivandrum IndiaSeptember 2011

[2] K Wang W Pei L Zou A Song and Z He ldquoOn the securityof 3D Cat map based symmetric image encryption schemerdquoPhysics Letters A vol 343 no 6 pp 432ndash439 2005

[3] J Li A Song and X Zhang ldquoHaptic texture rendering usingsingle texture imagerdquo in Proceedings of the 3rd International

Symposium on Computational Intelligence and Design (ISCIDrsquo10) pp 7ndash10 October 2010

[4] X Cindy Guo and D Hatzinakos ldquoImage authentication usingadded signal-dependent noiserdquo Journal of Electrical and Com-puter Engineering vol 2007 Article ID 47549 5 pages 2007

[5] X Zhang C Wang S Zhong and Q Yao ldquoImage encryptionscheme based on balanced two-dimensional cellular automatardquoMathematical Problems in Engineering vol 2013 Article ID562768 10 pages 2013

[6] G Yang H Jin andN Bai ldquoImage encryption using the chaoticJosephus matrixrdquo Mathematical Problems in Engineering vol2014 Article ID 632060 13 pages 2014

[7] J Zhang D Hou and H Ren ldquoImage encryption algorithmbased on dynamic DNA coding and Chenrsquos hyperchaotic sys-temrdquo Mathematical Problems in Engineering vol 2016 ArticleID 6408741 11 pages 2016

[8] W Wang D Peng H Wang H Sharif and H-H ChenldquoEnergy-constrained quality optimization for secure imagetransmission in wireless sensor networksrdquo Advances in Multi-media vol 2007 Article ID 25187 9 pages 2007


[9] I Maglogiannis ldquoTowards the adoption of open source andopen access electronic health record systemsrdquo Journal of Health-care Engineering vol 3 no 1 pp 141ndash161 2012

[10] J Zhang and Y Zhang ldquoAn image encryption algorithm basedon balanced pixel and chaotic maprdquo Mathematical Problems inEngineering vol 2014 Article ID 216048 7 pages 2014

[11] C Liu B Lu and H Li ldquoSecure access control and large scalerobust representation for online multimedia event detectionrdquoThe Scientific World Journal vol 2014 Article ID 219732 12pages 2014

[12] K Zhang and J-B Fang ldquoColor image encryption algorithmbased on TD-ERCS system and wavelet neural networkrdquoMath-ematical Problems in Engineering vol 2015 Article ID 50105410 pages 2015

[13] S S Askar A A Karawia and A Alshamrani ldquoImage encryp-tion algorithm based on chaotic economic modelrdquo Mathemat-ical Problems in Engineering vol 2015 Article ID 341729 10pages 2015

[14] A Kanso and M Ghebleh ldquoAn efficient and robust imageencryption scheme for medical applicationsrdquo Communicationsin Nonlinear Science and Numerical Simulation vol 24 no 1ndash3pp 98ndash116 2015

[15] G Chen Y Mao and C K Chui ldquoA symmetric image encryp-tion scheme based on 3D chaotic cat mapsrdquo Chaos Solitons andFractals vol 21 no 3 pp 749ndash761 2004

[16] P Tian-Gong and L Da-Yong ldquoA novel image encryption usingarnold catrdquo International Journal of Security and Its Applicationsvol 7 no 5 pp 377ndash386 2013

[17] V Patidar N K Pareek G Purohit and K K Sud ldquoArobust and secure chaotic standard map based pseudorandompermutation-substitution scheme for image encryptionrdquoOpticsCommunications vol 284 no 19 pp 4331ndash4339 2011

[18] H S Kwok and W K S Tang ldquoA fast image encryption systembased on chaotic maps with finite precision representationrdquoChaos Solitons amp Fractals vol 32 no 4 pp 1518ndash1529 2007

[19] V K Kushwaha and K Anusudha ldquoBased double encryptionapproach for secure transaction of medical imagesrdquo Interna-tional Journal of Advanced Research in Electrical Electronics andInstrumentation Engineering vol 2 no 4 pp 1418ndash1423 2013

[20] M Ahmad and T Ahmad ldquoA framework to protect patientdigital medical imagery for secure telediagnosisrdquo ProcediaEngineering vol 38 pp 1055ndash1066 2012

[21] A Al-Haj G Abandah and N Hussein ldquoCrypto-based algo-rithms for secured medical image transmissionrdquo IET Informa-tion Security vol 9 no 6 article 365 2015

[22] L O M Kobayashi S S Furuie and P S L M BarretoldquoProviding integrity and authenticity in DICOM images anovel approachrdquo IEEE Transactions on Information Technologyin Biomedicine vol 13 no 4 pp 582ndash589 2009

[23] X Q Zhou H K Huang and S L Lou ldquoAuthenticity andintegrity of digital mammography imagesrdquo IEEE Transactionson Medical Imaging vol 20 no 8 pp 784ndash791 2001

[24] H-M Chao C-M Hsu and S-G Miaou ldquoA data-hiding tech-nique with authentication integration and confidentiality forelectronic patient recordsrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 6 no 1 pp 46ndash53 2002

[25] S Gueron ldquoAES-GCM for efficient authenticated encryptionrdquoin Proceedings of theWorkshop on Real-World Cryptography pp1ndash32 January 2013

[26] D Brat Ojha A Sharma A Dwivedi B Kumar and A KumarldquoAn authenticated two-tier security on transmission of medical

image using codebase cryptosystem over teeming channelrdquoInternationnal Journal of Computer Applications vol 12 no 9pp 22ndash26 2011

[27] W Puech and J M Rodrigues ldquoA new crypto-watermarkingmethod for medical images safe transferrdquo in Proceedings of the12th European Signal Processing Conference (EUSIPCO rsquo04) pp1481ndash1484 Vienna Austria 2004

[28] F CaoH KHuang andXQ Zhou ldquoMedical image security inaHIPAAmandated PACS environmentrdquoComputerizedMedicalImaging and Graphics vol 27 no 2-3 pp 185ndash196 2003

[29] Z Hua Y Zhou C-M Pun andC L P Chen ldquo2D Sine Logisticmodulation map for image encryptionrdquo Information Sciencesvol 297 pp 80ndash94 2015

[30] M Francois T Grosges D Barchiesi and R Erra ldquoA newimage encryption scheme based on a chaotic functionrdquo SignalProcessing Image Communication vol 27 no 3 pp 249ndash2592012

[31] T Gao and Z Chen ldquoA new image encryption algorithm basedon hyper-chaosrdquo Physics Letters A vol 372 no 4 pp 394ndash4002008

[32] Y Zhou L Bao and C L P Chen ldquoA new 1D chaotic system forimage encryptionrdquo Signal Processing vol 97 pp 172ndash182 2014

[33] Y Zhou L Bao and C L P Chen ldquoImage encryption usinga new parametric switching chaotic systemrdquo Signal Processingvol 93 no 11 pp 3039ndash3052 2013

[34] C-J Cheng and C-B Cheng ldquoAn asymmetric image cryp-tosystem based on the adaptive synchronization of an uncertainunified chaotic system and a cellular neural networkrdquo Commu-nications inNonlinear Science andNumerical Simulation vol 18no 10 pp 2825ndash2837 2013

[35] K Jasteazebski and Z Kotulski ldquoOn improved image encryp-tion scheme based on chaotic map latticesrdquo Engineering Tran-scations vol 69 no 84 2009

[36] J B Lima F Madeiro and F J R Sales ldquoEncryption ofmedical images based on the cosine number transformrdquo SignalProcessing Image Communication vol 35 pp 1ndash8 2015

[37] C K Huang andH H Nien ldquoMulti chaotic systems based pixelshuffle for image encryptionrdquoOptics Communications vol 282no 11 pp 2123ndash2127 2009

[38] S Som and S Sen ldquoA non-adaptive partial encryption ofgrayscale images based on chaosrdquo Procedia Technology vol 10pp 663ndash671 2013

[39] G Alvarez and S Li ldquoBreaking an encryption scheme based onchaotic baker maprdquo Physics Letters Section A General Atomicand Solid State Physics vol 352 no 1-2 pp 78ndash82 2006

[40] N Kumar and H T Panduragha ldquoAdvanced partial imageencryption using two-stage hill cipher techniquerdquo IternationalJournal of Computer Applications vol 60 no 16 pp 14ndash19 2012

[41] X W Li S J Cho and S T Kim ldquoHigh security androbust optical image encryption approach based on computer-generated integral imaging pickup and iterative back-projectiontechniquesrdquo Optics and Lasers in Engineering vol 55 pp 162ndash182 2014

[42] C Ye Z Xiong Y Ding X Zhang G Wang and F XuldquoJoint fingerprintingencryption for medical image securityrdquoInternational Journal of Security and Its Applications vol 9 no1 pp 409ndash418 2015

[43] httpsenwikipediaorgwikiLanczos algorithm[44] J Zhang D Fang and H Ren ldquoImage encryption algorithm

based on DNA encoding and chaotic mapsrdquo MathematicalProblems in Engineering vol 2014 Article ID 917147 10 pages2014


[45] X Liao S Lai and Q Zhou ldquoA novel image encryptionalgorithm based on self-adaptive wave transmissionrdquo SignalProcessing vol 90 no 9 pp 2714ndash2722 2010

[46] Y Wu J P Noonan and S Agaian ldquoA wheel-switch chaoticsystem for image encryptionrdquo in Proceedings of the InternationalConference on System Science and Engineering (ICSSE rsquo11) pp23ndash27 Guiyang China June 2011

[47] Y Wu G Yang H Jin and J P Noonan ldquoImage encryptionusing the two-dimensional logistic chaotic maprdquo Journal ofElectronic Imaging vol 21 no 1 Article ID 013014 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



In this paper the authors addressed attacks such as statisticaland differential attacks Spatial permutation does not fit forpixel value modification in the image but it makes changesin pixel positions

Reference [3] applied a point-based interaction methodseffectively and feasibly to generate tangible textures fromstatic images and implemented a haptic virtual environmentbased on the OpenGL and PHANTOM Omni haptic devicefor the size of input image 128 times 128 However the proposedwork did not concentrate on security issues

The work by [4] explains a technique for image authenti-cation based on adding signal-dependent noise while takinginput image hidden noise was embedded into an image basedon film grain noise model Later original image and noiseare extracted for authentication purpose Here few attacksare addressed such as robust against content-preservingmodifications additive Gaussian noise local denoising anddetecting of malicious tampering Future work of this paperis to design an efficient noise filter for estimating the originalimage statistics

In [5] the authors presented a 2D image encryptionmethod based on balanced 2-Dimensional CellularAutomata(2DCA) Random image and original image are encrypted bypseudorandom number generator with a kernel value Theadvantages are as follows fast in encryption low-cost andlarge-size secret key Attacks addressed are such as statisticalanalysis correlation coefficients histogram analysis confu-sion analysis NPCR analysis and information entropy

In [6] a new image encryption has been proposed basedon chaotic Josephus matrix which extends the conventionalJosephus traversing method The future work of this papercan be applied to audio and video files for security purpose In[7] Lorenz Chaotic Scheme (LCS) and Chenrsquos hyperchaotic(CHC) method along with DNA sequences for an imageencryption algorithm that can dynamically select eight typesof DNA encryption rules and eight types of DNA additionand subtraction rules are used LCS was used to generatethe chaotic sequences to scramble the image CHC andDNA are used for image diffusion Here key size is 84 times10128 However authors have not addressed security issueshistogram analysis pixel correlation chart test and entropyIn [8] a new cross-layer unequal error protection (UEP) isintroduced which reduces image encryption overhead andcontrols the image bit stream structure to deliver the imagedata in wireless sensor networks This paper assures energycompetence and image security and quality over the imagetransmission in wireless network channels But the authorsdid not express their works on security issues such as brute-force attack key space analysis histogram analysis pixelcorrelation chaotic test and entropy

Reference [9] concentrates on open source EHRs alongwith parameters such as strengths weaknesses opportuni-ties threats of Electronic Health Record (EHR) over opensource EHRs and security services which are also notaddressed The work explained by [10] uses chaos mappingfunction to improve sensitivity of the initial state pixelposition changed by iterative function and XOR operationsfor diffusionThis paper combines chaos theory and iterativeequations based balanced pixel algorithm to decide the

number of iterations for the image encryption and resultantlow speed in image encryptionThe authors addressed in [11]tree proxy-based and service-oriented access control system(TPSACS) to fix secure detection of multimedia events inan online environment 1000 objects set as event block havebeen proposed to fix the scale robust illustration issue inonline services The future work can be applied in actionrecognition However security services are not addressed

Reference [12] proposed Tangent-Delay Ellipse ReflectingCavity-Map System (TD-ERC) wavelet neural networks(WNN) and XOR operations on binary data that achievescipher image Here addressed attacks are as follows keysize being 10195 histogram analysis correlation analysis anddifferential analysis The proposed system can be applied toprovide security for information Reference [13] introducedsymmetric chaotic economic map (CEM) with key space1084 the entropy that closes to ideal value 8 and low coef-ficient correlation that closes to 0 Initially CEM generateda chaotic sequence with fraction decimal values to integersAddressed attacks are key sensitivity analysis correlationanalysis and analysis of information entropy

In 2016 Kanso and Ghebleh [14] selected chaotic catmap algorithm used for medical image security applicationswith 119903 rounds and each round has two phases shuffling andmasking applied for block level as well as full image Themasking phase of each round uses a pseudorandom matrixof the same size as the input image to increase processingspeed Statistical cryptanalytic attacks such as key search anddifferential attacks are analyzed formedical image robustnessSame encryption and decryption technique are applied forROI as well as for full image and also achieved the same levelof security in ROI and full image Analyzed brute-force attackby considering key space is large However the author has notaddressed decrypted image quality and information entropy

In [15] 2-Dimensional Chaotic Map (2CDM) has beenconverted to 3-dimensional cat map (3DCM) for fast designand secure private image encryption with 128 bits Generallythe good cipher image will have less correlation amongpixels Here analyzed attacks are as follows statistical anddifferential attacks However brute-force and correlation ofimage attacks are not addressed This one is suitable for real-time Internet image security and telemedicine

In [16] a novel image encryption Using 3-dimensionalArnold cat map defends brute-force attack chosen-plaintextattack statistical attack and also image noise salt and peppernoise Gaussian noise and low-pass filter attacks Time takenfor encryption and decryption process for Lenna image (with256 times 256 sizes) was 0007 and 0012 seconds respectivelyBut chi-square test pixels correlation key space and entropyare not addressed

Reference [17] proposed pseudorandom permutationndashsubstitution method for image encryption based on loss-less symmetric block cipher The main design of proposedmethodwas to provide security for color image Computationspeed of encryption process has been increased by directlyshuffling row by row and column by column instead of pixelby pixel Security parameters are considered in the proposedmethod the histograms correlation coefficients informationentropy key sensitivity analysis differential analysis and key





















3 Proposed Method



1 3 4 1

4 2 2 2

3 1 1 4

2 4 3 3

23 8 48 10

37 17 83 54

199 66 101 93

247 71 107 252

23 66 107 10

247 17 83 54

199 8 48 252

37 71 101 93

Column Sorting

C C998400 I


I PM

1 3 4 1

4 2 2 2

3 1 1 4

2 4 3 3

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

10 3 4 15 8 13 6

2 15 11 12

7 14 4 9

I Pixel shuffling











119868 (119894 119895) = 119896 for 1198621015840 (119894 119895) = 119862 (119896 119895) (1)


119865 (119875 119868) = 119872 (2)



Column sorting

HCMT

GEM shuffling

Row sorting

Pixel confusion

Key matrix K

Lanczos algorithm

Calculate vector

characteristics

Start

End

Host image P



Z = Mlowast K






Step 1for 119894 = 1 2 3 119898 minus 1



25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(a)

25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(b)

500

400

300

200

100

0

0 50 100 150 200 250

0 50 100 150 200 250

600

500

400

300

200

100

0

(c)

0 50 100 150 200 250

1200

1000

800

600

400

200

0

0 50 100 150 200 250

600

500

400

300

200

100

0

(d)

0 50 100 150 200 250

4000

3500

3000

2500

2000

1500

1000

500

0


0 50 100 150 200 250

2500

2000

1500

1000

500

0



(e)









(a) (b) (c) (d)

(e) (f) (g) (h)









119862119903119903 =119864 (119883 minus 120583119883) (119884 minus 120583119884)

120590119883120590119884 (4)



119867(119896) = minus119899

sum119894=1

119875119903 (119896119894) log2119875119903 (119896119894) (5)





CMT [29]



3D chaoticmap [15]

Originalimage 091765 095415 090205

Cipherimage 001183 000016 001480

HCMT-EE






MSEdB (6)


MSE = 1119872119873

119872minus1

sum119909=0

119873minus1

sum119910=0

(119891 (119909 119910) minus 1198911015840 (119909 119910))2 (7)






5 Conclusion


Abbreviations









Competing Interests


References






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





























3 Proposed Method



1 3 4 1

4 2 2 2

3 1 1 4

2 4 3 3

23 8 48 10

37 17 83 54

199 66 101 93

247 71 107 252

23 66 107 10

247 17 83 54

199 8 48 252

37 71 101 93

Column Sorting

C C998400 I


I PM

1 3 4 1

4 2 2 2

3 1 1 4

2 4 3 3

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

10 3 4 15 8 13 6

2 15 11 12

7 14 4 9

I Pixel shuffling











119868 (119894 119895) = 119896 for 1198621015840 (119894 119895) = 119862 (119896 119895) (1)


119865 (119875 119868) = 119872 (2)



Column sorting

HCMT

GEM shuffling

Row sorting

Pixel confusion

Key matrix K

Lanczos algorithm

Calculate vector

characteristics

Start

End

Host image P



Z = Mlowast K






Step 1for 119894 = 1 2 3 119898 minus 1



25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(a)

25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(b)

500

400

300

200

100

0

0 50 100 150 200 250

0 50 100 150 200 250

600

500

400

300

200

100

0

(c)

0 50 100 150 200 250

1200

1000

800

600

400

200

0

0 50 100 150 200 250

600

500

400

300

200

100

0

(d)

0 50 100 150 200 250

4000

3500

3000

2500

2000

1500

1000

500

0


0 50 100 150 200 250

2500

2000

1500

1000

500

0



(e)









(a) (b) (c) (d)

(e) (f) (g) (h)









119862119903119903 =119864 (119883 minus 120583119883) (119884 minus 120583119884)

120590119883120590119884 (4)



119867(119896) = minus119899

sum119894=1

119875119903 (119896119894) log2119875119903 (119896119894) (5)





CMT [29]



3D chaoticmap [15]

Originalimage 091765 095415 090205

Cipherimage 001183 000016 001480

HCMT-EE






MSEdB (6)


MSE = 1119872119873

119872minus1

sum119909=0

119873minus1

sum119910=0

(119891 (119909 119910) minus 1198911015840 (119909 119910))2 (7)






5 Conclusion


Abbreviations









Competing Interests


References






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 3 4 1

4 2 2 2

3 1 1 4

2 4 3 3

23 8 48 10

37 17 83 54

199 66 101 93

247 71 107 252

23 66 107 10

247 17 83 54

199 8 48 252

37 71 101 93

Column Sorting

C C998400 I


I PM

1 3 4 1

4 2 2 2

3 1 1 4

2 4 3 3

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

10 3 4 15 8 13 6

2 15 11 12

7 14 4 9

I Pixel shuffling











119868 (119894 119895) = 119896 for 1198621015840 (119894 119895) = 119862 (119896 119895) (1)


119865 (119875 119868) = 119872 (2)



Column sorting

HCMT

GEM shuffling

Row sorting

Pixel confusion

Key matrix K

Lanczos algorithm

Calculate vector

characteristics

Start

End

Host image P



Z = Mlowast K






Step 1for 119894 = 1 2 3 119898 minus 1



25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(a)

25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(b)

500

400

300

200

100

0

0 50 100 150 200 250

0 50 100 150 200 250

600

500

400

300

200

100

0

(c)

0 50 100 150 200 250

1200

1000

800

600

400

200

0

0 50 100 150 200 250

600

500

400

300

200

100

0

(d)

0 50 100 150 200 250

4000

3500

3000

2500

2000

1500

1000

500

0


0 50 100 150 200 250

2500

2000

1500

1000

500

0



(e)









(a) (b) (c) (d)

(e) (f) (g) (h)









119862119903119903 =119864 (119883 minus 120583119883) (119884 minus 120583119884)

120590119883120590119884 (4)



119867(119896) = minus119899

sum119894=1

119875119903 (119896119894) log2119875119903 (119896119894) (5)





CMT [29]



3D chaoticmap [15]

Originalimage 091765 095415 090205

Cipherimage 001183 000016 001480

HCMT-EE






MSEdB (6)


MSE = 1119872119873

119872minus1

sum119909=0

119873minus1

sum119910=0

(119891 (119909 119910) minus 1198911015840 (119909 119910))2 (7)






5 Conclusion


Abbreviations









Competing Interests


References






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Column sorting

HCMT

GEM shuffling

Row sorting

Pixel confusion

Key matrix K

Lanczos algorithm

Calculate vector

characteristics

Start

End

Host image P



Z = Mlowast K






Step 1for 119894 = 1 2 3 119898 minus 1



25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(a)

25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(b)

500

400

300

200

100

0

0 50 100 150 200 250

0 50 100 150 200 250

600

500

400

300

200

100

0

(c)

0 50 100 150 200 250

1200

1000

800

600

400

200

0

0 50 100 150 200 250

600

500

400

300

200

100

0

(d)

0 50 100 150 200 250

4000

3500

3000

2500

2000

1500

1000

500

0


0 50 100 150 200 250

2500

2000

1500

1000

500

0



(e)









(a) (b) (c) (d)

(e) (f) (g) (h)









119862119903119903 =119864 (119883 minus 120583119883) (119884 minus 120583119884)

120590119883120590119884 (4)



119867(119896) = minus119899

sum119894=1

119875119903 (119896119894) log2119875119903 (119896119894) (5)





CMT [29]



3D chaoticmap [15]

Originalimage 091765 095415 090205

Cipherimage 001183 000016 001480

HCMT-EE






MSEdB (6)


MSE = 1119872119873

119872minus1

sum119909=0

119873minus1

sum119910=0

(119891 (119909 119910) minus 1198911015840 (119909 119910))2 (7)






5 Conclusion


Abbreviations









Competing Interests


References






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(a)

25

2

15

1

05

0

0 1

times104

times104

10

8

6

4

2

0

0 1

(b)

500

400

300

200

100

0

0 50 100 150 200 250

0 50 100 150 200 250

600

500

400

300

200

100

0

(c)

0 50 100 150 200 250

1200

1000

800

600

400

200

0

0 50 100 150 200 250

600

500

400

300

200

100

0

(d)

0 50 100 150 200 250

4000

3500

3000

2500

2000

1500

1000

500

0


0 50 100 150 200 250

2500

2000

1500

1000

500

0



(e)









(a) (b) (c) (d)

(e) (f) (g) (h)









119862119903119903 =119864 (119883 minus 120583119883) (119884 minus 120583119884)

120590119883120590119884 (4)



119867(119896) = minus119899

sum119894=1

119875119903 (119896119894) log2119875119903 (119896119894) (5)





CMT [29]



3D chaoticmap [15]

Originalimage 091765 095415 090205

Cipherimage 001183 000016 001480

HCMT-EE






MSEdB (6)


MSE = 1119872119873

119872minus1

sum119909=0

119873minus1

sum119910=0

(119891 (119909 119910) minus 1198911015840 (119909 119910))2 (7)






5 Conclusion


Abbreviations









Competing Interests


References






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c) (d)

(e) (f) (g) (h)









119862119903119903 =119864 (119883 minus 120583119883) (119884 minus 120583119884)

120590119883120590119884 (4)



119867(119896) = minus119899

sum119894=1

119875119903 (119896119894) log2119875119903 (119896119894) (5)





CMT [29]



3D chaoticmap [15]

Originalimage 091765 095415 090205

Cipherimage 001183 000016 001480

HCMT-EE






MSEdB (6)


MSE = 1119872119873

119872minus1

sum119909=0

119873minus1

sum119910=0

(119891 (119909 119910) minus 1198911015840 (119909 119910))2 (7)






5 Conclusion


Abbreviations









Competing Interests


References






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












CMT [29]



3D chaoticmap [15]

Originalimage 091765 095415 090205

Cipherimage 001183 000016 001480

HCMT-EE






MSEdB (6)


MSE = 1119872119873

119872minus1

sum119909=0

119873minus1

sum119910=0

(119891 (119909 119910) minus 1198911015840 (119909 119910))2 (7)






5 Conclusion


Abbreviations









Competing Interests


References






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Competing Interests


References






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









a fast enhanced secure image chaotic cryptosystem based on hybrid chaotic magic...

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