Security Analysis on an ElGamal-Like Multivariate Encryption Scheme Based on Isomorphism of Polynomials

Yasuhiko Ikematsu, Shuhei Nakamura, Bagus Santoso, Takanori Yasuda

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

Abstract

Isomorphism of polynomials with two secrets (IP2S) problem was proposed by Patarin et al. at Eurocrypt 1996 and the problem is to find two secret linear maps filling in the gap between two polynomial maps over a finite field. At PQC 2020, Santoso proposed a problem originated from IP2S, which is called block isomorphism of polynomials with circulant matrices (BIPC) problem. The BIPC problem is obtained by linearizing IP2S and restricting secret linear maps to linear maps represented by circulant matrices. Using the commutativity of products of circulant matrices, Santoso also proposed an ElGamal-like encryption scheme based on the BIPC problem. In this paper, we give a new security analysis on the ElGamal-like encryption scheme. In particular, we introduce a new attack (called linear stack attack) which finds an equivalent key of the ElGamal-like encryption scheme by using the linearity of the BIPC problem. We see that the attack is a polynomial-time algorithm and can break some 128-bit proposed parameters of the ElGamal-like encryption scheme within 10 h on a standard PC.

Original languageEnglish
Title of host publicationInformation Security and Cryptology - 17th International Conference, Inscrypt 2021, Revised Selected Papers
EditorsYu Yu, Moti Yung
PublisherSpringer Science and Business Media Deutschland GmbH
Pages235-250
Number of pages16
ISBN (Print)9783030883225
DOIs
Publication statusPublished - 2021
Event17th International Conference on Information Security and Cryptology, Inscrypt 2021 - Virtual, Online
Duration: Aug 12 2021Aug 14 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13007 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference17th International Conference on Information Security and Cryptology, Inscrypt 2021
CityVirtual, Online
Period8/12/218/14/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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