On plateaued functions

Yuliang Zheng, Xian Mo Zhang

Research output: Contribution to journalArticlepeer-review

107 Citations (Scopus)
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The focus of this correspondence is on nonlinear characteristics of cryptographic Boolean functions. First, we introduce the notion of plateaued functions that have many cryptographically desirable properties. Second, we establish a sequence of strengthened inequalities on some of the most important nonlinearity criteria, including nonlinearity, avalanche, and correlation immunity, and prove that critical cases of the inequalities coincide with characterizations of plateaued functions. We then proceed to prove that plateaued functions include as a proper subset all partially bent functions that were introduced earlier by Claude Carlet. This solves an interesting problem that arises naturally from previously known results on partially bent functions. In addition, we construct plateaued, but not partially bent, functions that have many properties useful in cryptography.

Original languageEnglish
Pages (from-to)1215-1223
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number3
Publication statusPublished - 2001

Bibliographical note

Copyright 2001 IEEE. Reprinted from IEEE Transactions on information theory. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Macquarie University’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it


  • Bent functions
  • cryptography
  • nonlinear characteristics
  • partially bent functions
  • plateaued functions


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