Cryptology ePrint Archive: Report 2018/796
On relations between CCZ- and EA-equivalences
Lilya Budaghyan and Marco Calderini and Irene Villa
Abstract: In the present paper we introduce some sufficient conditions and a procedure for checking whether, for a given function, CCZ-equivalence is more general than EA-equivalence together with taking inverses of permutations. It is known from Budaghyan, Carlet and Pott (2006) and Budaghyan, Carlet and Leander (2009) that for quadratic APN functions (both monomial and polynomial cases) CCZ-equivalence is more general. We prove hereby that for non-quadratic APN functions CCZ-equivalence can be more general (by studying the only known APN function which is CCZ-inequivalent to both power functions and quadratics). On the contrary, we prove that for pawer no-Gold APN functions, CCZ equivalence coincides with EA-equivalence and inverse transformation for $n\le 8$. We conjecture that this is true for any $n$.
Category / Keywords: secret-key cryptography / CCZ-equivalence, EA-equivalence, APN, Boolean functions
Date: received 30 Aug 2018
Contact author: marco calderini at uib no
Available format(s): PDF | BibTeX Citation
Version: 20180901:122359 (All versions of this report)
Short URL: ia.cr/2018/796
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