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On relations between CCZ- and EA-equivalences

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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 et al. (IEEE Trans. Inf. Theory 52.3, 1141–1152 2006; Finite Fields Appl. 15(2), 150–159 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 power non-Gold APN functions, CCZ equivalence coincides with EA-equivalence and inverse transformation for n ≤ 8. We conjecture that this is true for any n.

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Correspondence to Marco Calderini.

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Budaghyan, L., Calderini, M. & Villa, I. On relations between CCZ- and EA-equivalences. Cryptogr. Commun. 12, 85–100 (2020). https://doi.org/10.1007/s12095-019-00367-5

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Keywords

  • CCZ-equivalence
  • EA-equivalence
  • APN
  • Boolean functions

Mathematics Subject Classification (2010)

  • 94A60
  • 06E30
  • 11T71