Undeniable signature scheme based over group ring

D. Chaum and H. van Antwerpen first introduced the concept of an undeniable signature scheme where the verification step is verified with the signer’s co-operation. In this paper, first we discuss a combination of Discrete Logarithm Problem (DLP) and Conjugacy Search Problem (CSP) analysing its security. Then we propose an undeniable signature scheme in a non-abelian group over group ring whose security relies on difficulty of the combination of the DLP and the CSP. The complexity and security of our proposed scheme has also been discussed.

[1]  N. Koblitz A Course in Number Theory and Cryptography , 1987 .

[2]  Tony Thomas,et al.  A Zero-knowledge Undeniable Signature Scheme in Non-abelian Group Setting , 2008, Int. J. Netw. Secur..

[3]  D. Passman,et al.  The algebraic structure of group rings , 1977 .

[4]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[5]  A. Myasnikov,et al.  Non-Commutative Cryptography and Complexity of Group-Theoretic Problems , 2011 .

[6]  Yehuda Lindell,et al.  Introduction to Modern Cryptography (Chapman & Hall/Crc Cryptography and Network Security Series) , 2007 .

[7]  Meinolf Geck,et al.  Group representation theory , 2007 .

[8]  Yehuda Lindell,et al.  Introduction to Modern Cryptography , 2004 .

[9]  Mohammad Eftekhari A Diffie-Hellman Key Exchange Using Matrices Over Non Commutative Rings , 2012 .

[10]  Mohammad Eftekhari,et al.  A Diffie–Hellman key exchange protocol using matrices over noncommutative rings , 2012, Groups Complex. Cryptol..

[11]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[12]  Douglas R. Stinson,et al.  Cryptography: Theory and Practice,Second Edition , 2002 .

[13]  Tzer-Shyong Chen,et al.  A New Elliptic Curve Undeniable Signature Scheme , 2006 .

[14]  Jonathan Katz,et al.  Introduction to Modern Cryptography: Principles and Protocols , 2007 .

[15]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[16]  Delaram Kahrobaei,et al.  Public key exchange using matrices over group rings , 2013, Groups Complex. Cryptol..

[17]  Hugo Krawczyk,et al.  RSA-Based Undeniable Signatures , 1997, Journal of Cryptology.

[18]  Delaram Kahrobaei,et al.  NIS05-6: A Non-Commutative Generalization of ElGamal Key Exchange using Polycyclic Groups , 2006, IEEE Globecom 2006.

[19]  Gerrit Bleumer,et al.  Undeniable Signatures , 2011, Encyclopedia of Cryptography and Security.

[20]  Eligijus Sakalauskas,et al.  Key Agreement Protocol (KAP) Using Conjugacy and Discrete Logarithm Problems in Group Representation Level , 2007, Informatica.