Multivariate Public Key Cryptography

Abstract

A multivariate public key cryptosystem (MPKCs for short) have a set of (usually) quadratic polynomials over a finite field as its public map. Its main security assumption is backed by the NP-hardness of the problem to solve nonlinear equations over a finite field. This family is considered as one of the major families of PKCs that could resist potentially even the powerful quantum computers of the future. There has been fast and intensive development in Multivariate Public Key Cryptography in the last two decades. Some constructions are not as secure as was claimed initially, but others are still viable. The paper gives an overview of multivariate public key cryptography and discusses the current status of the research in this area.