Improved upper bound on the nonlinearity of high order correlation immune functions

Yuliang Zheng, Xian Mo Zhang

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

35 Citations (Scopus)

Abstract

It has recently been shown that when m > (Formula Presented)-1, the nonlinearity Nf of an mth-order correlation immune function f with n variables satisfies the condition of Nf ≤ 2n−1 − 2m, and that when m > 1(Formula Presented) − 2 and f is a balanced function, the nonlinearity satisfies Nf ≤ 2n−1 − 2m+1. In this work we prove that the general inequality, namely Nf ≤ 2n−1 − 2m, can be improved to Nf ≤ 2n−1 − 2m+1 for m ≥ 0.6n − 0.4, regardless of the balance of the function. We also show that correlation immune functions achieving the maximum nonlinearity for these functions have close relationships with plateaued functions. The latter have a number of cryptographically desirable properties.

Original languageEnglish
Title of host publicationSelected Areas in Cryptography - 7th Annual International Workshop, SAC 2000, Proceedings
PublisherSpringer, Springer Nature
Pages262-274
Number of pages13
Volume2012
ISBN (Print)354042069X, 9783540420699
Publication statusPublished - 2001
Event7th Annual International Workshop on Selected Areas in Cryptography, SAC 2000 - Waterloo, Canada
Duration: 14 Aug 200015 Aug 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2012
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other7th Annual International Workshop on Selected Areas in Cryptography, SAC 2000
Country/TerritoryCanada
CityWaterloo
Period14/08/0015/08/00

Keywords

  • Correlation Immune Functions
  • Nonlinearity
  • Plateaued Functions
  • Resilient Functions
  • Stream Ciphers

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