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.

On relations between CCZ- and EA-equivalences / Budaghyan, L.; Calderini, M.; Villa, I.. - In: CRYPTOGRAPHY AND COMMUNICATIONS. - ISSN 1936-2447. - 12:1(2020), pp. 85-100. [10.1007/s12095-019-00367-5]

On relations between CCZ- and EA-equivalences

Calderini M.;Villa I.
2020

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.
1
Budaghyan, L.; Calderini, M.; Villa, I.
On relations between CCZ- and EA-equivalences / Budaghyan, L.; Calderini, M.; Villa, I.. - In: CRYPTOGRAPHY AND COMMUNICATIONS. - ISSN 1936-2447. - 12:1(2020), pp. 85-100. [10.1007/s12095-019-00367-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/328828
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