Relationships among nonlinearity criteria

Jennifer Seberry, Xian Mo Zhang, Yuliang Zheng

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

20 Citations (Scopus)


An important question in designing cryptographic functions including substitution boxes (S-boxes) is the relationships among the various nonlinearity criteria each of which indicates the strength or weakness of a cryptographic function against a particular type of cryptanalytic attacks. In this paper we reveal, for the first time, interesting connections among the strict avalanche characteristics, differential characteristics, linear structures and nonlinearity of quadratic S-boxes. In addition, we show that our proof techniques allow us to treat in a unified fashion all quadratic permutations, regardless of the underlying construction methods. This greatly simplifies the proofs for a number of known results on nonlinearity characteristics of quadratic permutations. As a by-product, we obtain a negative answer to an open problem regarding the existence of differentially 2-uniform quadratic permutations on an even dimensional vector space.

Original languageEnglish
Title of host publicationAdvances in Cryptology - EUROCRYPT 1994 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
PublisherSpringer, Springer Nature
Number of pages13
ISBN (Print)3540601767, 9783540601760
Publication statusPublished - 1995
EventWorkshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1994 - Perugia, Italy
Duration: 9 May 199412 May 1994

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)03029743
ISSN (Electronic)16113349


OtherWorkshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1994


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