Paper title: An Elgamal Encryption Scheme of Fibonacci Q-Matrix and Finite State Machine
DOI: https://doi.org/10.4316/JACSM.201502002
Published in: Issue 2, (Vol. 9) / 2015Download
Publishing date: 2015-10-22
Pages: 13-17
Author(s): Kumar B. Ravi , Sekhar A. Chandra , Naidu G. Appala
Abstract. Cryptography is the science of writing messages in unknown form using mathematical models. In Cryptography, several ciphers were introduced for the encryption schemes. Recent research focusing on designing various mathematical models in such a way that tracing the inverse of the designed mathematical models is infeasible for the eve droppers. In the present work, the ELGamal encryption scheme is executed using the generator of a cyclic group formed by the points on choosing elliptic curve, finite state machines and key matrices obtained from the Fibonacci sequences
Keywords: ElGamal, Fibonacci Sequence, Finite State Machine, Encryption, Decryption
References:

1. N.Koblitz. Elliptic curve Cryptosystems. Mathematics of computation, 48, 203-209, 1987. 2. A textbook of Guide to elliptic curve cryptography by Darrel Hancott Vanstone 1965.

3. N. Koblitz. Hyper Elliptic Cryptosystem. International Journal of Cryptography, 1,139-150,1989.

4. A Course in Number Theory and Cryptography. By Neal Koblitz, 1994.

5. V. Miller. Uses of Elliptic Curves in Cryptography. In Advances in Cryptology (CRYPTO-1985).

6. A textbook of Cryptography and Network Security by William Stallings, 2011.

7. An introduction to the theory of elliptic curves by Joseph H.Silverman brown University and NTRU Cryptosystems2006.

8. Vorobyov NN. Fibonacci numbers. Moscow: Nauka; 1978 in Russian.

9. Hoggat VE. Fibonacci and Lucas numbers. Palo Alto, CA: Houghton- Mifflin; 1969.

10. S. Fibonacci and Lucas numbers and the golden section. Theory and applications Ellis Horwood limited; 1989.

11. Stakhov AP. Introduction into algorithmic measurement theory. Moscow: Soviet Radio; 1977 in Russian.

12. A.P. Stakhov, “The ‘‘golden’’ matrices and a newkind of cryptography”, Chaos, Solutions and Fractals 32 (2007) pp1138–1146.

13. Stakhov AP. A generalization of the Fibonacci Q-matrix. Rep Natl Acad Sci Ukraine1999 (9):46 9.9(9)46-49.

14. K.R.Sudha, A. Chandra Sekhar, Prasad Reddy P VG D “Cryptography Protection of Digital Signals using Some Recurrence Relations” International Journal of Computer Science andNetwork Security,Vol.7 No.5, May 2007.

15. Adesh K.Pandey reprint 2009, “An introduction to automata theory and formal languages S.K.Karana & sons. New Delhi.

16. Johan E.Hopcroft, Rajeev Motwin, Jeffrey D.Uiman. “Introduction to automata theory, language, and computation” Vanstone 3 rd impression, 2007 CRC press, Dorling Kindersley (India) Pvt.Ltd.

17. T.ElGamal,“A public-key cryptosystem and a signature scheme based on discrete logarithms ” IEEE Transactions on Information Theory, onInformation Theory, 469-472, 1985.

18. P.A.Jyotirmie, B.Ravi Kumar, A.Chandra Sekhar,S.Uma Devi “A one to one Correspondence inelliptic curve cryptography” InternationalJournal of Mathematical archive-4(3), 2013:300- 304.

19. http://www.certicom.com/index.php/ecc-tutorial.

20. B.Ravi Kumar, A. Chandra Sekhar, G.Appala Naidu “An ElGamal Encryption Scheme of Adjacency Matrix and Finite Machines” COMPUSOFT, An international Journal of advanced computer technology, Volume 4, Issue 3, March 2015, pages 1548-1554.

21. 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, Volume 20, Number 2, Feb 2015, pages 70-73.

22. B.Ravi Kumar, A. Chandra Sekhar, G.Appala Naidu “An Elgamal Encryption of Finite State Machines and points on the Elliptic Curve” Journal of theoretical Physics & Cryptography, Volume 9, July 2015, pages 1-5.

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