Paper 2018/796

On relations between CCZ- and EA-equivalences

Lilya Budaghyan, Marco Calderini, and Irene Villa


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 $n$.

Available format(s)
Secret-key cryptography
Publication info
Preprint. MINOR revision.
CCZ-equivalenceEA-equivalenceAPNBoolean functions
Contact author(s)
marco calderini @ uib no
2018-09-01: received
Short URL
Creative Commons Attribution


      author = {Lilya Budaghyan and Marco Calderini and Irene Villa},
      title = {On relations between CCZ- and EA-equivalences},
      howpublished = {Cryptology ePrint Archive, Paper 2018/796},
      year = {2018},
      note = {\url{}},
      url = {}
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