Revisiting the minrank problem on multivariate cryptography

Yacheng Wang, Yasuhiko Ikematsu, Shuhei Nakamura, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The minrank problem is often considered in the cryptanalysis of multivariate cryptography and code-based cryptography. There have been many multivariate cryptosystems proven insecure due to their weakness against the minrank attack, which is an attack that transforms breaking a cryptosystem into solving a minrank problem instance. In this paper, we review two existing methods, the Kipnis-Shamir method (KS), and minors modeling for solving a minrank instance, and then propose a mixed method that merges these two methods. Our method uses a bilinear subsystem from the KS method and a subsystem from minors modeling. It is at least as effective as the KS method, and does not require as many minors as minors modeling. Moreover, we consider applying the hybrid approach on multivariate polynomials solved in our mixed method to further improve our method. We then revisit the minrank attack on Rainbow and conclude the previous complexity analysis of the minrank attack on Rainbow is overestimated, and provide the correct complexity of the minrank attack on NIST PQC 2nd round Rainbow parameters.

Original languageEnglish
Title of host publicationInformation Security Applications - 21st International Conference, WISA 2020, Revised Selected Papers
EditorsIlsun You
PublisherSpringer Science and Business Media Deutschland GmbH
Pages291-307
Number of pages17
ISBN (Print)9783030652982
DOIs
Publication statusPublished - 2020
Event21st International Conference on Information Security Applications, WISA 2020 - Jeju Island, Korea, Republic of
Duration: Aug 26 2020Aug 28 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12583 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International Conference on Information Security Applications, WISA 2020
CountryKorea, Republic of
CityJeju Island
Period8/26/208/28/20

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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