Cryptology ePrint Archive: Report 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.

Category / Keywords: Affine equivalence, Almost perfect nonlinear, Bent function, Boolean function, CCZ-equivalence, Nonlinearity

Date: received 9 Feb 2009, last revised 16 Feb 2009

Contact author: Lilya Budaghyan at ii uib no

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Note: Corrected misprints

Version: 20090216:122122 (All versions of this report)

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