Abstract

Braid groups were first introduced by Emil Artin in 1925. First cryptosystem, using Braid groups as a platform was discovered by Anshel et al in 2001. After the publication of this paper several cryptosystems on Braid groups had been designed. In this paper we have proposed a tripartite authenticated key agreement protocol using conjugacy problem which works in a braid group. We have proved that our protocol meet the security attributes under the assumption that the Conjugacy Search Problem (CSP) is hard in braid group.

References

• Anshel, M.Anshel, B.Fisher,and D.Goldfeld, New key agreement protocols in braid group cryptography, Proc.of CT-RSA 2001,LNCS, 2020,Springer-Verlag, 1-15.
• Anshel, M. Anshel and D. Goldfeld, An algebraic method of public-key cryptography, Math. Research Letters, 6 (1999), 287-291.
• E. Artin, Theory of braids, Annals of Math.48 (1947),101-126.
• J. Birman, Braids, Links, and Mapping Class Groups, Annals of Math. Studies, Princeton Univ. Press (1975).
• Atul Chaturvedi and Sunder Lal, An authenticated key agreement protol using conjugacy problem in braid groups, International Journal of Network security, Vol. 6, No. 2, pp. 181 – 184, Mar. 2008. (http://ijns.nchu.edu.tw/)
• M.M. Chowdhury, On the security of new key exchange protocols based on the triple decomposition problem, preprint 2007, http://www.aexiv.org/abs/cs.CR/0611065.
• M.M. Chowdhury, An authentication scheme using non – commutative semi groups, ieeexplore.ieee.org,2007.
• F. A. Garside, The braid group and other groups, Quart. J. Math. Oxford 20-78(1969) 235-254.
• K.H.Ko, D.H.Choi, M.S.Cho, and J.W.Lee, New signature scheme using conjugacy problem, (http://eprint.iacr.org/2002/168).
• K.H. KO, S.J. Lee, J.H. Cheon, J.W. Han, J.S. Kang, and C Park, New public-key cryptosystem using braid groups, Advances in Cryptology, Proceeding of Crypto - 2000, Lecture Notes in Computer Science 1880, ed. M Bellore, springs Verlag (2000), 166-183.
• A. G. Myasnikov, V. Shpilrain and A. Ushakov, Group – based cryptography, Birkhauser, 2008.
• V. Shpilrain and A. Ushakov, A new key exchange protocol based on the decomposition problem, contemp. Math. 418 (2006) , 161 – 167.
• V. Shpilrain and A. Ushakov, An authentication scheme based on the twisted conjugacy problem, preprint (2008), http://arxiv.org/pdf/math.GR/0805.2701.
• H. Sibert, P. Dehornoy, & M. Girault, Entity authentication schemes using braid word reduction,” in International Workshop on Coding and Cryptography (WCC) 2003, Discrete Applied Mathematics, 154-2, Elsevier, 420 – 436 (2006). (http://eprint.iacr.org/2002/187).
• B. C. Wang, Y. P. Hu, Sinature scheme based on the root extraction problem over braid groups, ieeexplore.ieee.org, 2009
• S. B. Wilson, and A. Menezes, “ Autenticated Diffie – Hellman key agreement protocols”, Proceedings of the 5th Annual Workshop on Selected aeas in Cryptography (SAC’ 98), LNCS, pp. 339 – 361, 1999.
• S. B. Wilson, D. Johnson and A. Menezes, Key agreement protocol and their security analysis”, Proceedings of the 6th IMA International Conference on Cryptography and Coding, Vol. 1355, LNCS, pp. 339 – 361, Springer – Verlag, 1998.
• W. Yun, X . Gua – Hua, Z. Xing – Kai , B. Wan. Security analysis and design ofproxy signature schemes over braid groups, http://eprint.iacr.org/2009/458
• W. Yun, X . Gua – Hua, Z. Xing – Kai , B. Wan. A strong blind signature scheme over braid groups, http://eprint.iacr.org/2009/622.
• W. Yun, G. Xiong, W. Bao, and X. Zhang, A ring signature scheme over braid groups, Journal of Electronics, 27 (4), 522 – 527,2010.