Construction of Multivariate Quadratic Quasigroups (MQQs) in arbitrary Galois fields

Abstract

In this paper we describe two methods for constructing Multivariate Quadratic Quasigroups (MQQ) in Galois fields of any characteristic and order. Our constructions extend the previously known constructions defined for operations over the prime field of characteristic 2. Application of these new constructions can reduce the public key size of the recently introduced family of public key schemes based on MQQs up to 58 times.