An Improved affine equivalence algorithm for random permutations

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

Abstract

In this paper we study the affine equivalence problem, where given two functions F,G: {0, 1}n → {0, 1}n, the goal is to determine whether there exist invertible affine transformations A1,A2 over GF(2)n such that G = A2°F°A1Algorithms for this problem have several wellknown applications in the design and analysis of Sboxes, cryptanalysis of white-box ciphers and breaking a generalized Even-Mansour scheme. We describe a new algorithm for the affine equivalence problem and focus on the variant where F,G are permutations over n-bit words, as it has the widest applicability. The complexity of our algorithm is about n32n bit operations with very high probability whenever F (or G) is a random permutation. This improves upon the best known algorithms for this problem (published by Biryukov et al. at EUROCRYPT 2003), where the first algorithm has time complexity of n322nnd the second has time complexity of about n323n/2 and roughly the same memory complexity. Our algorithm is based on a new structure (called a rank table) which is used to analyze particular algebraic properties of a function that remain invariant under invertible affine transformations. Besides its standard application in our new algorithm, the rank table is of independent interest and we discuss several of its additional potential applications.

Original languageEnglish
Title of host publicationAdvances in Cryptology - EUROCRYPT 2018 - 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2018 Proceedings
EditorsJesper Buus Nielsen, Vincent Rijmen
PublisherSpringer Verlag
Pages413-442
Number of pages30
ISBN (Print)9783319783802
DOIs
StatePublished - 1 Jan 2018
Event37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2018 - Tel Aviv, Israel
Duration: 29 Apr 20183 May 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10820 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2018
Country/TerritoryIsrael
CityTel Aviv
Period29/04/183/05/18

Keywords

  • Affine equivalence problem
  • Block cipher
  • Cryptanalysis
  • Even-Mansour cipher
  • Rank table

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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