Key Exchange Protocol Based on the Matrix Power Function Defined Over "Equation missing"

Abstract

AbstractIn this paper we propose a key exchange protocol (KEP) based on the so-called matrix power function (MPF) defined over a non-commuting platform group. In general, it is not possible to construct KEP using a non-commuting platform group. Therefore we proposed special templates for our public parameters thus allowing us to construct KEP relying on the basic properties of our MPF. Security analysis is based on the decisional Diffie-Hellman (DDH) attack game. We proved that the distribution of the entries of the public session parameter matrices and the shared key matrix asymptotically approaches to uniform with exponential rate. Hence proposed KEP is secure under the DDH assumption. This implies that our protocol is not vulnerable to the computational Diffie-Hellman (CDH) attack. We presented the evidence of CDH security by numerical simulation of linearization attack and showed that it is infeasible.KeywordsNon-commutative cryptographyMatrix power functionKey exchange protocol