A NON-REPUDIABLE BIASED BITSTRING KEY-AGREEMENT PROTOCOL WITH
ROOT PROBLEM IN NON-ABELIAN GROUP

Abhishek Dwivedi; D.B.Ojha

A NON-REPUDIABLE BIASED BITSTRING KEY-AGREEMENT PROTOCOL WITH ROOT PROBLEM IN NON-ABELIAN GROUP

Abhishek Dwivedi^*1 and D.B.Ojha²

Research Scholar Singhania University, Jhunjhunu, Rajsthan& Department of M.C.A, Raj Kumar Goel Engineering College, Ghaziabad, U.P., India dwivediabhi@gmail.com
Department of Mathematics, R. K. G. Institute of Technology, Ghaziabad, U.P., India ojhdb@yahoo.co.in

Corresponding Author: Abhishek Dwivedi, E-mail: dwivediabhi@gmail.com

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Abstract

The Key exchange problems are of central interest in security world. The basic aim is that two people who can only communicate via an insecure channel want to find a common secret key without any attack. In this paper, we elaborated the process for well secured and assured for sanctity of correctness about the sender’s and receiver’s identity, as non-repudiable biased bitstring key agreement protocol using root problem in non-abelian group (NKR-NAG).

Keywords

Diffie-Hellman key Agreement, Root Problem, Braid Groups, Protocol Crypto--graphy, Key Distribution Center (KDC), Non-Abelian Group.

INTRODUCTION

A common cryptographic technique to encrypt each individual conversation with a separate key. This is called a session key, because it is used for only one particular communication session,[3].In this protocol we assume Alice & bob are users of network ,each share secret key with the KDC(Trent).This protocol relies on the absolute security of Trent. Here we also assume Mallory is a lot more powerful than Eve if Mallory corrupt Trent, the whole network is compromised. This is known as man –in-the-middle attack and Alice & Bob have no way to verify that they are talking to each other. The problem in [12] sets around for our work, in Ko et al [6] proposed a braid group version of Diffie-Hellman key agreement, Manin- the- middle attack works on this protocol. Since the path breaking work of Diffie -Hellman in 1976, several key agreement protocols have been proposed over the years [7, 8, 1, 11, 2, 9, and 10]. We improve the above scheme by proposing a biased key agreement protocol based on RP in non-abelian groups (NKR-NAG). We make use of Root Problem (RP) to suggest a new key agreement scheme. The RP in braid groups is algorithmically difficult and consequently provides one-way functions. In proposed scheme, we establish a new security pole for improve man- inthe- middle attack. So that Mallory can’t impersonation between communicate parties. Braid Group has good enough candidature for choosing it as a non abelian group.

PRELIMINARIES

BRAID GROUPS:

Emil Artin [5] in 1925 defined , the braid group of index n, using following generators and relations: Consider the

DIFFIE-HELLMAN KEY AGREEMENT (DHKA)

Key Agreement

SECURITY ANALYSIS

Here we prove our protocol meets the following desirable attributes for essential security analysis.

CONCLUSION

Non-repudiable key agreement protocols are an essential part of secure e-gaming and e-gambling protocols. In fact, such protocols are a guarantee that player misbehaviours or deviations from the protocols will be detected. Using the new primitive, one party is allowed to agree on the same value to both party with a given, fixed bias while the basic bitstring can be viewed as special case when the bias value is set to 1/ 2. Using a public key cryptosystem to construct a shared key is away of achieving non-repudiability, a property which cannot be offered by hash functions alone. In this paper, we have presented a non-repudiable biased bitstring key agreement protocol that allows both players to share a bitstring in a nonrepudiable way based on the braid root problems with 1/ k – biased bitstring.

In this paper, specially, the key sharing process will be start after being assured about the perfectness of sender’s and receiver’s identity. Hence, our proposed scheme is well secured and assured for sanctity of correctness about the sender’s and receiver’s identity.

References

Menezes, M. Qu, and S. Vanstone, “Key agree-ment andthe need for authentication,” in Proceedings of PKS’95,pp. 34-42, 1995.
AtulChaturvedi, Sunderlal” An Authenticated KeyAgreement Protocol Using Conjugacy Problem in BraidGroups” in International Journal of Network SecurityVol.6 No.2 p.p. 181-184, March, 2008.
Bruce Schneier “applied cryptography, second edition”John wiley&sons, Inc.
D.B.Ojha, J.P.Pandey, Ajay Sharma, and AbhishekDwivedi, “A non-repudiable biased bitstring commitmentscheme on a post quantum cryptosystem” Journal ofTheoretical and Applied Information Technology, Vol.12, No.1, 2010.
E. Artin, “Theory of braids,” Annals of Mathematics, vol.48, pp. 101-126, 1947.
K. Ko, S. Lee, J. Cheon, J. Han, J. kang C. Park. Newpublic key cryptosystem using braid groups, Crypto’2000,LNCS 1880, pp.166-183, Springer 2000.
L. Law, A. Menezes, M. Qu, J. Solinas, and S. Van-stone,An Efficient Protocol for Authenticated Key Agreement,Technical Report CORR98-05, Department of CO,University of Waterloo, 1998.
L. Law, A. Menezes, M. Qu, J. Solinas, and S. Van-stone,“An efficient protocol for authenticated key agreement,”Design, Codes and Cryptography, Vol.28, no. 2, pp. 119-134, 2003.
M. Bellare, A. Desai, D. Pointcheval and P. Rogaway,Relations among notions of security for public-keyencryption schemes, Advances in Cryptology | CRYPTO'98, Lecture Notes in Computer Science, 1462 (1998),Springer-Verlag, pp. 26-45.
R.Dutta, R. Barua and P. Sarkar,”Pairing BasedCryptography: A Survey Cryptology e-print Archive”,Report 2004/064, 2004.
S. B. Wilson, D.Johnson, and A. Menezes,“Keyagreement protocol and their security analysis,” inProceedings of Sixth IMA International Conference onCryptography and Coding, pp. 30-45, 1997.
W. Diffie and M.Hellman, “New directions incryptography,” IEEE Transactions on InformationTheory, Vol. 22, no. 6, pp. 644-654, 1976.