A Novel ElGamal Encryption Scheme of Elliptic Curve Cryptography

International Journal of Computer Trends and Technology (IJCTT)          
© 2015 by IJCTT Journal
Volume-20 Number-2
Year of Publication : 2015
Authors : B. Ravi Kumar , A. Chandra Sekhar , G.Appala Naidu


B. Ravi Kumar , A. Chandra Sekhar , G.Appala Naidu "A Novel ElGamal Encryption Scheme of Elliptic Curve Cryptography". International Journal of Computer Trends and Technology (IJCTT) V20(2):70-73, Feb 2015. ISSN:2231-2803. www.ijcttjournal.org. Published by Seventh Sense Research Group.

Abstract -
Cryptography is the art of using mathematical models to encrypt and decrypt data. Cryptography enables to store sensitive information or transmit across insecure networks so that it cannot be read by anyone except the intended recipient. Ever since the inception of Cryptography, several efficient encryption schemes were introduced by the researches. Among such one is the ElGamal encryption scheme. In the present work, the ElGamal encryption scheme is proposed using the points on an elliptic curve and as an additional security the Fibonacci Q-matrix is introduced.

[1] N. Koblitz. Elliptic curve Cryptosystems. Mathematics of computation, 48203-209, 1987.
[2] A text book of Guide to elliptic curve Cryptography by Darrel Hancott Vanstone.
[3] N. Koblitz. Hyper Elliptic Cryptosystem, International Journal of Cryptography, 1,139-150,189.
[4] A Course in Number Theory and Cryptography. By Neal Koblitz.
[5] V. Miller. Uses of Elliptic Curves in Cryptography. In Advances in (CRYPTO 1985), Springer LNCS, 218, 417–426, 1985.
[6] A text book of Cryptography and Network Security by William Stallings.
[7] An introduction to the theory of elliptic curves by Joseph H. Silverman brown University and NTRU Cryptosystems.
[8] A Course in Number Theory and Cryptography –second edition by Neal Koblitz
[9] J ElGamal. A public key Cryptosystem and a signature scheme based on discrete logarithms.In Advances Cryptology (CRYPTO 1984), Springer.
[10] Vorobyov NN. Fibonacci numbers, Moscow: Nauka; 1978 [in Russian].
[11] Hogget VE. Fibonacci and Lucas numbers.Palo Alto,CA: Houghton- Mifflin; 1969.
[12] Vajda S. Fibonacci and Lucas numbers and the golden section. Theory and applications. Ellis Horwood limited; 1989.
[13] Stakhov AP. Introduction into algorithmic measurement theory. Moscow: Soviet Radio; 1977 [in Russian].
[14] A.P. Stakhov,”The ‘‘golden’’ matrices and a new kind of cryptography”, Chaos, Solutions and Fractals 32 (2007) pp1138–1146.
[15] Stakhov OP.A generalization of the Fibonacci Q-matrix.Rep Nat Acad Sci Ukraine1999 (9):46-9.
[16] Stakhov AP. The golden section and modern harmony mathematics. Applications of Fibonacci numbers,7. Kluwer Academic Publishers; 1998.p.393-99.
[17] A. Chandra Sekhar, S. Uma Devi “A one to one Correspondence in elliptic curve cryptography” International Journal of Mathematical archive-4(3), 2013:300-304.
[18] http://www.certicom.com/index.php/ecc-tutorial.
[19] K.R.Sudha, A.chandra Sekhar ,Prasad Reddy P.V.G.D. “Cryptography protection of Digital Signals using some recurrence relations” International Journal of Computer Science and Network Security, Vol (7) no 5 m may 2007,203-207.
[20] T. ElGamal, “A public-key cryptosystem and a signature scheme based on discrete logarithms”, IEEE Transactions on Information Theory, on Information Theory, 469- 472, 1985.

ElGaml, Recurrence relation, Fibonacci sequence.