A new key exchange protocol based on the decomposition problem

In this paper we present a new key establishment protocol based on the decomposition problem in non-commutative groups which is: given two elements $w, w_1$ of the platform group $G$ and two subgroups $A, B \subseteq G$ (not necessarily distinct), find elements $a \in A, b \in B$ such that $w_1 = a w b$. Here we introduce two new ideas that improve the security of key establishment protocols based on the decomposition problem. In particular, we conceal (i.e., do not publish explicitly) one of the subgroups $A, B$, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a given finitely generated subgroup.Comment: 7 page

Key Exchange in Elliptic Curve Cryptography Based on the Decomposition Problem

ABSTRACT In this paper, we presented a new key exchange method based on decomposition problem for elliptic curve cryptography. We showed that our key exchange method was not only an alternative method for designing keys in cryptography, but it also has improved security condition from the previous key exchange based on decomposition problem over noncommutative groups. We proposed elliptic an curve cryptography to be the new platform for our key exchange protocol and showed how it was implemented. The security of our protocol was based on discrete logarithm problem, which was not infeasible and strictly difficult to retrieve in elliptic curve cryptography without any prior knowledge. Keyword

Double shielded Public Key Cryptosystems

By introducing extra shields on Shpilrain and Ushakov\u27s Ko-Lee-like protocol based on the decomposition problem of group elements we propose two new key exchange schemes and then a number of public key cryptographic protocols. We show that these protocols are free of known attacks. Particularly,if the entities taking part in our protocols create their private keys composed by the generators of the Mihailova subgroups of Bn, we show that the safety of our protocols are very highly guarantied by the insolvability of subgroup membership problem of the Mihailova subgroups

Public Key Protocols over Twisted Dihedral Group Rings

Key management is a central problem in information security. The development of quantum computation could make the protocols we currently use unsecure. Because of that, new structures and hard problems are being proposed. In this work, we give a proposal for a key exchange in the context of NIST recommendations. Our protocol has a twisted group ring as setting, jointly with the so-called decomposition problem, and we provide a security and complexity analysis of the protocol. A computationally equivalent cryptosystem is also proposed