Paper 2009/063

CCZ-equivalence and Boolean functions

Lilya Budaghyan and Claude Carlet

Abstract

We study further CCZ-equivalence of $(n,m)$-functions. We prove that for Boolean functions (that is, for $m=1$), CCZ-equivalence coincides with EA-equivalence. On the contrary, we show that for $(n,m)$- functions, CCZ-equivalence is strictly more general than EA-equivalence when $n\ge5$ and $m$ is greater or equal to the smallest positive divisor of $n$ different from 1. Our result on Boolean functions allows us to study the natural generalization of CCZ-equivalence corresponding to the CCZ-equivalence of the indicators of the graphs of the functions. We show that it coincides with CCZ-equivalence.

Note: Corrected misprints

Metadata
Available format(s)
PDF PS
Publication info
Published elsewhere. Unknown where it was published
Keywords
Affine equivalenceAlmost perfect nonlinearBent functionBoolean functionCCZ-equivalenceNonlinearity
Contact author(s)
Lilya Budaghyan @ ii uib no
History
2009-02-16: last of 2 revisions
2009-02-10: received
See all versions
Short URL
https://ia.cr/2009/063
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2009/063,
      author = {Lilya Budaghyan and Claude Carlet},
      title = {CCZ-equivalence and Boolean functions},
      howpublished = {Cryptology ePrint Archive, Paper 2009/063},
      year = {2009},
      note = {\url{https://eprint.iacr.org/2009/063}},
      url = {https://eprint.iacr.org/2009/063}
}
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