A New Key Exchange Protocol Based on Infinite Non-Abelian Groups

Abstract

In order to resist quantum attacks, a key exchange protocol based on infinite non-abelian groups is proposed in this paper. For the purpose, by the composition of twice the operation of a semidirect product, we construct a shared secret key which contains two hard problems of equivalent decomposition problem (EDP) and discrete logarithm problem (DLP). Then, two methods，algebra attack and brute force attack, were employed to verify the antiattack for the proposed protocol. By a sound mathematical inference, it demonstrates that the proposed protocol possesses security positively. Finally, we analyzed the computational complexity and bit complexity when the protocol being implemented on braid groups, and furthermore, the complexity data confirm the feasibility of establishing the key exchange protocol there. Thus, in any case, security or complexity, the actual use of the proposed protocol means achievable in practice.