A Non-Linear Variant of Elliptic Curve Cryptography with Quadratic Residues over Finite Field
Keywords:
Cryptography, Decryption, Encryption, Functions, Elliptic curve cryptography, Finite fieldAbstract
In the digital world security issues play an important role in data communications over unreliable network. Cryptography is most useful technique for transferring data in secure manner, the data sent is extremely expected to be received by authorized person over the public network. Since the Elliptic curve cryptography is introduced in 1985, elliptic curves have simulated a lot of research works in public key cryptography. At present, several cipher systems have been developed based on the Elliptic Curve Cryptography(ECC) for the purpose of secure data transformation. As security of ECC is related to hardness of discrete logarithm problem on elliptic curve (ECDLP) and there are endless possibilities to create cipher system using ECC we have used elliptic curves in a different way from the way in traditional ECC. In this paper, we have proposed a cipher system, called Quadratic Residue Non- linear Variant to ECC over the finite field to intensify security and privacy
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References
Neal Koblitz, “Elliptic Curve Cryptosystems,” Mathematics of Computation, vol. 48, issue 177, pp. 203–209, January 1987.
S. Miller Victor, "Use of elliptic curves in cryptography," In Advances in Cryptology-CRYPTO'85 Proceedings, Springer Berlin Heidelberg, pp. 417-426. 1985.
D. Sravana Kumar, Ch. Suneetha and A. Chandrasekhar. “ Encryption of Data Using Elliptic Curve Over Finite Fields,” International Journal of Distributed and Parallel Systems (IJDPS), no. 1, vol. 3, January 2012.
Lo’ai Tawalbeh, Moad Mowafi and Walid Aljoby. “Use of Elliptic Curve Cryptography for Multimedia Encryption,” IET Information Security, vol. 7, issue 2, pp. 67–74, 2012.
Koblitz Neal, Alfred Menezes and Scott Vanstone. “The state of elliptic curve cryptography,” In Towards a quarter - century of public key cryptography, Springer US, pp. 103-123, 2000.
K. Koyama, U.M.Maurer, T. Okamoto and S.A. Vanstone, “New Public-Key Schemes Based on Elliptic Curves over the Ring〖 Z〗_n,” In Annual International Cryptology Conference; Lecture Notes in Computer Science 576, Springer, Berlin/Heidelberg, Germany, pp. 252–266, 1991.
C. Couvreur and J.J. Quisquater, “ Fast Decipherment Algorithm for RSA Public-Key Cryptosystem,” Electron. Lett., vol.18, pp. 905–907, 1982.
Maher Boudabra and Abderrahmane Nitaj, “A New RSA Variant Based on Elliptic Curves,” Cryptography 2023, 7, 37.
S. Ullah, J. Zhen and N. Din et al, “Elliptic Curve Cryptography, Applications, challenges, recent advances, and future trends: A comprehensive survey,” Computer Science Review 47, 2023.
R. Rivest, A. Shamir and L. Adleman, “A Method for Obtaining signatures and public-key cryptosystems,” Commun. ACM, vol. 21, pp. 120–126, 1978.
H.M. Sun, M.E. Wu, W.C. Ting and M.J. Hinek, “Dual RSA and its security analysis,” Digital IEEE Trans. Inf. Theory, vol. 53, 2007.
N. Koblitz, “Elliptic curve cryptosystems,” Math. Comput., Vol. 48, pp. 203–209, 1987.
Laiphrakpam Dolendro Sing and Khumanthem Manglem Singh, “Implementation of Text Encryption using Elliptic Curve Cryptography,” Eleventh International Multi-Conference on Information Processing-2015 (IMCIP-2015) Procedia Computer Science, vol. 54, pp, 73 - 82, 2015.
S. Maria Celestin Vigila and K. Muneeswaran, “Implementation of Text based Cryptosystem using Elliptic Curve Cryptography,” International Conference on Advanced Computing, IEEE, pp. 82–85, December 2009.
T. El-Gamal, "A public key cryptosystem and a signature scheme based on the discrete logarithm," IEEE Transactions on Information Theory, vol. 31, no. 1, pp. 469-472, 1985.
Scott A. Vansfone, “Elliptic Curve Cryptography-The Answer to Strong, Fast Public-Key Cryptography for Securing Constrained Environments,” Information Security Technical Report, vol. 2, no. 2, pp. 78–87, 1997.
O. Srinivasa Rao and S. Pallam Setty, “Efficient Mapping Methods for Elliptic Curve Cryptography,” International Journal of Engineering Science and Technology, vol. 2, pp. 3651–3656, 2010.
Nakamoto. S. Bitcoin, “A Peer-to-Peer Electronic Cash System,” 2009, Available online: https://bitcoin.org/bitcoin.pdf.
Neal Koblitz, A Course in Number Theory and Cryptography. Second edition , Springer-Verleg, 1994.
Lawrence C. Washington, Elliptic curves: Number Theory and Cryptography. Second edition, Chapman & Hall/CRC, New York, 2006.
M. Hinek, Cryptanalysis of RSA and its Variants. Cryptography and Network Security Series, Chapman & Hall/CRC Press, Boca Raton, FL, USA, 2009.
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