KEY EXCHANGE PROTOCOL USING DECOMPOSITION PROBLEM IN NEAR-RING

Abstract

There are several public key cryptosystem around that use computational hardness of either conjugacy search problem or the word problem for non-abelian groups. In this paper we use decomposition problem in near-ring to construct a public key cryptosystem and improved the security of key establishment protocol based on the decomposition problem.

Keywords

• public key cryptosystem,near-ring,decomposition problem,key exchange protocol

Near-Ring

Abstract

References

1. Anshel, I., Anshel, M., Fisher, B. and Goldfeld, D., “ New key agreement protocols in braid group cryptography”, In D. Naccache (editor), Topics in Cryptology – CTRSA 2001, volume 2020 of Lecture Notes in Computer Science, SpringerVerlag, Berlin, 13–27, (2001).
2. Anshel, I., Anshel M. and Goldfeld D., “An algebraic method for public-key cryptography”, Mathematical Research Letters, 1–5, (1999).
3. Bell, Howard E., and Steve Ligh, “Some decomposition theorems for periodic rings and near-rings”, Math. J. Okayama Univ 31, (1989), 93-99.
4. Cannon, Alan G., “Centralizer near-rings determined by End G, Springer Netherlands”, (1995).
5. Cao Z., “Conic analog of RSA cryptosystem and some improved RSA cryptosystems”, Journal of Natrual Science of Heilongjiang University, (1999).
6. Cao Z., “A threshold key escrow scheme based on public key cryptosystem”, Science in China , 441-448, (2001).
7. Diffie W. and Hellman M.E., “New directions in cryptography”, IEEE Transactions on Information Theory 22, 644-654, (1976).
8. Eftekhari, Mohammad, “A Diffie–Hellman key exchange protocol using matrices over noncommutative rings”, Groups-Complexity-Cryptology 4.1, 167-176, (2012).

9. Ferrero, Giovanni, “Near-rings: some developments linked to semigroups and groups”, Springer Science & Business Media, (2013).
10. Gentry C. and Szydlo M., “Cryptanalysis of the revised NTRU signature scheme”, In L. Knudsen (editor), Advances in Cryptology – EUROCRYPT 2002, volume 2332 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 299–320 ,(2002).
11. Gentry C., “Key recovery and message attacks on NTRU-composite”, In B. Pfitzmann (editor), Advances in Cryptology – EUROCRYPT 2001, volume 2045 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 182–194, (2001).
12. Hoffstein J., Pipher J. and Silverman J. H, “NTRU: a ring-based public key cryptosystem”, In J. P. Buhler (editor), Algorithmic Number Theory, volume 1423 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 267–288 ,(1998).
13. Hurley, Barry, and Ted Hurley, “Group ring cryptography”, arXiv preprint, (2011).
14. Ko K.H, Lee S.J, Cheon J.H, Han J.W, Kang J.s and Park C., “New public-key cryptosystem using braid groups”, In M. Bellare (editor), Advances in Cryptology – CRYPTO 2000, volume 1880 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 166–183, (2000).
15. Ko K.H, Lee J.W, and Thomas T., “Towards generating secure keys for braid cryptography. Designs”, Codes and Cryptography, 317–333, (2007),.
16. Ko, Ki Hyoung, “New public-key cryptosystem using braid groups”, Advances in cryptology—CRYPTO 2000. Springer Berlin Heidelberg, (2000).
17. Odoni R. W. K., Varadharajan V. and Sanders P. W., “Public key distribution in matrix rings”, Electronics Letters, 20, 386–387, (1984).
18. Rivest R.L., Shamir A. and Adleman L., “A method for obtaining digital signatures and public key cryptosystems”, Communications of the ACM 21, 120- 126, (1978).
19. Rabin M.O., “Digitized signatures and public-key functions as intractable as factorization”, MIT Laboratory for Computer Science Technical Report, LCS/TR-212 (1979).
20. Williams H.C., “A Modification of the RSA Public-Key Encryption Procedure”, IEEE Transactions on Information Theory, IT No.6 (26), 726-729, (1980).
21. Williams H.C., “Some public-key crypto-funtions as intractible as factorization”, In G.R. Blakley and D.Chaum (Eds): CRYPTO’84, LNCS 196, Springer-Verlag, 66-70, (1985).
22. Yagisawa, Masahiro, “Key Agreement Protocols Using Multivariate Equations on Non-commutative Ring”, IACR Cryptology ePrint Archive (2010) .