A cryptosystem with noncommutative platform groups

This paper presents a new public key cryptosystem that uses noncommutative groups as platform group. The underlying hard problem of the proposed cryptosystem is a combination of discrete log problem and conjugacy search problem. Due to use of noncommutative platform groups, it is expected that the presented cryptosystem provides higher levels of security against known attacks. Some important issues regarding the choice of platform and parameters of this cryptosystem are addressed. Further, a brief analysis of security aspects is also presented.

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

[2]  Neal R. Wagner,et al.  A Public Key Cryptosystem Based on the Word Problem , 1985, CRYPTO.

[3]  M. Hall The Theory Of Groups , 1959 .

[4]  D. M. Clark Theory of Groups , 2012 .

[5]  Vladimir Shpilrain Cryptanalysis of Stickel's Key Exchange Scheme , 2008, CSR.

[6]  T. Elgamal A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[7]  Ciaran Mullan,et al.  Some Results in Group-Based Cryptography , 2011 .

[8]  Elaine B. Barker,et al.  SP 800-131A. Transitions: Recommendation for Transitioning the Use of Cryptographic Algorithms and Key Lengths , 2011 .

[9]  Alfred Menezes,et al.  The Discrete Logarithm Problem in GL(n, q) , 1997, Ars Comb..

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

[11]  Sangjin Lee,et al.  Potential Weaknesses of the Commutator Key Agreement Protocol Based on Braid Groups , 2002, EUROCRYPT.

[12]  D. Goldfeld,et al.  An algebraic method for public-key cryptography , 1999 .

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

[14]  Zhenfu Cao,et al.  New public key cryptosystems based on non-Abelian factorization problems , 2013, Secur. Commun. Networks.

[15]  Dennis Hofheinz,et al.  A Practical Attack on Some Braid Group Based Cryptographic Primitives , 2003, Public Key Cryptography.

[16]  Alexander Ushakov,et al.  Cryptanalysis of the Anshel-Anshel-Goldfeld-Lemieux Key Agreement Protocol , 2009, Groups Complex. Cryptol..

[17]  A. Myasnikov,et al.  Group-based Cryptography , 2008 .

[18]  Eberhard Stickel,et al.  A New Method for Exchanging Secret Keys , 2005, Third International Conference on Information Technology and Applications (ICITA'05).

[19]  Taher ElGamal,et al.  A public key cyryptosystem and signature scheme based on discrete logarithms , 1985 .

[20]  Jung Hee Cheon,et al.  New Public-Key Cryptosystem Using Braid Groups , 2000, CRYPTO.