matrix based efficient ecc technique for …...on matrix approach for elliptic curve...
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International Journal of Advanced Computational Engineering and Networking, ISSN: 2320-2106, Volume-2, Issue-9, Sept.-2014
Matrix Based Efficient ECC Technique For Text Encryption
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MATRIX BASED EFFICIENT ECC TECHNIQUE FOR TEXT ENCRYPTION
1HITESH KAG, 2RUCHI TELANG GODE
1,2Department of Applied Mathematics, Defence Institute of Advanced Technology, Pune-411025, INDIA
E-mail: [email protected], [email protected]
Abstract- We propose a novel mapping method based on invertible matrix and random sequence for converting alphanumeric characters of the plaintext message onto the (x; y) coordinates of Elliptic Curve defined over the prime eld GF(p). The mapped points are further encrypted with Elgamal Cryptosystem. Finally we illustrate the implementation of our cryptosystem based into an elliptic curve characterized by the equation y2 = x3 - x + 19 (mod 71). The cryptosystem provides sufficient security against cryptanalysis at low computational overhead, a brute force attack to break the cryptosystem is almost infeasible. Keywords- Elgamal Encryption, Elliptic Curve Cryptography, Public key, Mapping Method. CRYPTOGRAPHY FOR ELLIPTIC CURVES Elliptic Curve Cryptography(ECC) was introduced in 1986 by Victor Miller [3] and Neil Kolbitz [4] as an alternative to other established public key cryptosystem such as RSA, Elgamal Cryptosystems, etc. The mathematical background of ECC is more complex and thus it provides greater security and more efficient performance than other rst generation public key cryptosys tems. With elliptic curves one of the main advantage is that the similar level of security can be achieved with considerably shorter keys than in methods based on the difficulties of solving discrete logarithms over integers or integer factorizations. The result is faster implementations, bandwidth savings, smaller key sizes, these features are especially attractive for security applications where computational power and integrated circuit space is limited, such as smart cards, personal digital assistants, and wireless devices. I. INTRODUCTION
II. PRELIMINARIES
International Journal of Advanced Computational Engineering and Networking, ISSN: 2320-2106, Volume-2, Issue-9, Sept.-2014
Matrix Based Efficient ECC Technique For Text Encryption
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III. PROPOSED MAPPING METHOD
International Journal of Advanced Computational Engineering and Networking, ISSN: 2320-2106, Volume-2, Issue-9, Sept.-2014
Matrix Based Efficient ECC Technique For Text Encryption
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The above set of mapped points can be encrypted by the encryption technique. Once the mapping of the all alphanumeric characters onto the curve is completed, these points are encrypted by using Elgamal encryption technique and are transmitted through an insecure channel. The message is retrieved from the encrypted data by using the Elgamal decryption technique followed by the application of the inverse of mapping method. IV. ENCRYPTION AND DECRYPTION
ALGORITHM
Finally by applying the inverse of the mapping method and discrete logarithm concept, it is possible to evaluate the ASCII value and thereby recover the plaintext. Hence the keys are transformed over the Elliptic Curve field for both encryption and decryption. The method promises to afford maximum security from intruders and hackers. V. IMPLEMENTATION OF THE MAPPING
METHOD AND ENCRYPTION ALGORITHM
Original message \ENHANCE" will be recovered using discrete logarithm concept since Bob knows the base point P and ASCII values.
International Journal of Advanced Computational Engineering and Networking, ISSN: 2320-2106, Volume-2, Issue-9, Sept.-2014
Matrix Based Efficient ECC Technique For Text Encryption
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CONCLUSIONS
REFERENCES
[1] F. Amounas and E.H. El Kinani, \Fast Mapping Method based on Matrix Approach For Elliptic Curve Cryptography," International Journal of Information and Network Security (IJINS) vol.1, no.2, pp. 54-59, June 2012, ISSN: 2089-3299.
[2] F. Amounas and E.H. El Kinani, \An Efficient Elliptic Curve Cryptography protocol Based on Matrices," International Journal of Engineering Inventions vol. 1, issue 9, pp. 49-54, November 2012.
[3] V.S. Miller, Use of Elliptic Curves in Cryptography. Advances in Cryptology CRYPTO'85, LNCS.218, New York, Springer-Verlag, pp. 417-426, 1986.
[4] Koblitz N., Menezes A.J., and Vanstone S.A. \The state of elliptic curve cryptography. Design, Codes and Cryptography," vol 19, issue 2-3, pp. 173-193, 2000.
[5] W. Stein. SAGE Mathematical Software, 2007, version 2.6, available at http://www.sagemath.org/