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
-
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},
url = {https://eprint.iacr.org/2009/063}
}
