Links among impossible differential, integral and zero correlation linear cryptanalysis

Bing Sun, Zhiqiang Liu, Vincent Rijmen, Ruilin Li, Lei Cheng, Qingju Wang, Hoda Alkhzaimi, Chao Li

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


As two important cryptanalytic methods, impossible differential and integral cryptanalysis have attracted much attention in recent years. Although relations among other cryptanalytic approaches have been investigated, the link between these two methods has been missing. The motivation in this paper is to fix this gap and establish links between impossible differential cryptanalysis and integral cryptanalysis. Firstly, by introducing the concept of structure and dual structure, we prove that a → b is an impossible differential of a structure E if and only if it is a zero correlation linear hull of the dual structure E. Meanwhile, our proof shows that the automatic search tool presented by Wu and Wang could find all impossible differentials of both Feistel structures with SP-type round functions and SPN structures. Secondly, by establishing some boolean equations, we show that a zero correlation linear hull always indicates the existence of an integral distinguisher. With this observation we improve the number of rounds of integral distinguishers of Feistel structures, CAST-256, SMS4 and Camellia. Finally, we conclude that an r-round impossible differential of E always leads to an r-round integral distinguisher of the dual structure ɛ. In the case that ɛ and ɛ are linearly equivalent, we derive a direct link between impossible differentials and integral distinguishers of ɛ. Our results could help to classify different cryptanalytic tools and facilitate the task of evaluating security of block ciphers against various cryptanalytic approaches.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology - CRYPTO 2015 - 35th Annual Cryptology Conference, Proceedings
EditorsMatthew Robshaw, Rosario Gennaro
PublisherSpringer Verlag
Number of pages21
ISBN (Print)9783662479889
StatePublished - 2015
Event35th Annual Cryptology Conference, CRYPTO 2015 - Santa Barbara, United States
Duration: Aug 16 2015Aug 20 2015

Publication series

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


Other35th Annual Cryptology Conference, CRYPTO 2015
Country/TerritoryUnited States
CitySanta Barbara


  • ARIA
  • CAST-256
  • Camellia
  • Feistel
  • Impossible differential
  • Integral
  • SMS4
  • SPN
  • Zero correlation linear

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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