The kth-order nonhomomorphicity of S-boxes

Yuliang Zheng*, Xian Mo Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Nonhomomorphicity is a new nonlinearity criterion of a mapping or S-box used in a private key encryption algorithm. An important advantage of nonhomomorphicity over other nonlinearity criteria is that the value of nonhomomorphicity is easy to estimate by the use of a fast statistical method. Due to the Law of Large Numbers, such a statistical method is highly reliable. Major contributions of this paper are (1) to explicitly express the nonhomomorphicity by other nonlinear characteristics, (2) to identify tight upper and lower bounds on nonhomomorphicity, and (3) to find the mean of nonhomomorphicity over all the S-boxes with the same size. It is hoped that these results on nonhomomorphicity facilitate the analysis and design of S-boxes.

Original languageEnglish
Pages (from-to)830-848
Number of pages19
JournalJournal of Universal Computer Science
Issue number8
Publication statusPublished - 2000


  • Boolean Functions
  • Cryptanalysis
  • Cryptography
  • Nonhomomorphicity
  • S-boxes

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