Recent Developments in Multivariate Public Key Cryptosystems

Yasufumi Hashimoto

doi:10.1007/978-981-15-5191-8_16

Abstract

AbstractThe multivariate signature schemes UOV, Rainbow, and HFEv- have been considered to be secure and efficient enough under suitable parameter selections. In fact, several second round candidates of NIST’s standardization project of Post-Quantum Cryptography are based on these schemes. On the other hand, there are few multivariate encryption schemes expected to be practical and despite that, various new schemes have been proposed recently. In the present paper, we summarize multivariate schemes UOV, Rainbow, and (variants of) HFE generating the second round candidates and study the practicalities of several multivariate encryption schemes proposed recently.

Highlights

In 2016, NIST launched the standardization project of Post-Quantum Cryptography (NIST 2020)
A lot of schemes were submitted to the first round of its project and 26 of them were chosen as the second round candidates in 2019 (NIST 2020)
LUOV (Beullens et al 2020), Rainbow (Ding et al 2020) and GeMSS (Casanova et al 2020) are multivariate signature schemes in the second round. These schemes are based on UOV (Kipnis et al 1999; Patarin 1997), Rainbow (Ding et al 2005), and HFEv(Patarin et al 2001), respectively, which were proposed before or around 2000 and have been still considered to be secure and efficient enough under suitable parameter

Summary

Introduction

In 2016, NIST launched the standardization project of Post-Quantum Cryptography (NIST 2020). LUOV (Beullens et al 2020), Rainbow (Ding et al 2020) and GeMSS (Casanova et al 2020) are multivariate signature schemes in the second round These schemes are based on UOV (Kipnis et al 1999; Patarin 1997), Rainbow (Ding et al 2005), and HFEv(Patarin et al 2001), respectively, which were proposed before or around 2000 and have been still considered to be secure and efficient enough under suitable parameter. 2 the schemes UOV (Kipnis et al 1999; Patarin 1997), Rainbow (Ding et al 2005), and (variants of) HFE (Patarin 1996) with short surveys on the second round candidates LUOV (Beullens et al 2020), Rainbow (Ding et al 2020), and GeMSS (Casanova et al 2020). We describe UOV (Kipnis et al 1999; Patarin 1997), Rainbow (Ding et al 2005), and variants of HFE (Patarin 1996) and give short surveys on the second round candidates LUOV (Beullens et al 2020), Rainbow (Ding et al 2020), and GeMSS (Casanova et al 2020) of NIST’s project (NIST 2020). We first propose the basic constructions of multivariate public key cryptosystems (MPKCS)

Basic Constructions of Multivariate Public Key Cryptosystems

We will discuss them in the individual schemes

Rainbow

Variants of HFE

New Encryption Schemes

Conclusion