An Improvement of a Key Exchange Protocol Relying on Polynomial Maps

Abstract

Akiyama et al. (Int. J. Math. Indust., 2019) proposed a post-quantum key exchange protocol that is based on the hardness of solving a system of multivariate non-linear polynomial equations but has a design strategy different from ordinary multivariate cryptography. However, their protocol has a drawback that the probability of failing to establish a common key is impractically high. In this paper, we improve the success probability of Akiyama et al.'s key exchange protocol significantly while keeping the security, by restricting each component of the correct common key from the whole of the coefficient field to its small subset. We give theoretical and experimental evaluations showing that our proposed parameter set for our protocol is expected to achieve both failure probability 2 −120 and 128-bit security level.