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On the Δ-equivalence of Boolean functions

Authors
  • Logachev, Oleg A.1
  • Fedorov, Sergey N.1
  • Yashchenko, Valerii V.1
  • 1 Information Security Institute of Lomonosov University, Russia , (Russia)
Type
Published Article
Journal
Discrete Mathematics and Applications
Publisher
De Gruyter
Publication Date
Apr 28, 2020
Volume
30
Issue
2
Pages
93–101
Identifiers
DOI: 10.1515/dma-2020-0009
Source
De Gruyter
Keywords
License
Yellow

Abstract

A new equivalence relation on the set of Boolean functions is introduced: functions are declared to be Δ-equivalent if their autocorrelation functions are equal. It turns out that this classification agrees well with the cryptographic properties of Boolean functions: for functions belonging to the same Δ-equivalence class a number of their cryptographic characteristics do coincide. For example, all bent-functions (of a fixed number of variables) make up one class.

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