Abstract
Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to the APN Gold function $${x^{2^r+1}}$$ if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2 n where n � 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.