Paper 2019/1355

A Nonlinear Multivariate Cryptosystem Based on a Random Linear Code

Daniel Smith-Tone and Cristina Tone

Abstract

We introduce a new technique for building multivariate encryption schemes based on random linear codes. The construction is versatile, naturally admitting multiple modifications. Among these modifications is an interesting embedding modifier--- any efficiently invertible multivariate system can be embedded and used as part of the inversion process. In particular, even small scale secure multivariate signature schemes can be embedded producing reasonably efficient encryption schemes. Thus this technique offers a bridge between multivariate signatures, many of which have remained stable and functional for many years, and multivariate encryption, a historically more troubling area.