Bracken, Carl, Byrne, Eimear, McGuire, Gary and Nebe, Gabriele (2011) On the Equivalence of Quadratic APN Functions. Designs, Codes and Cryptography, 61 (3). pp. 261-272. ISSN 0925-1022
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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 x2r+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 2n
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.
Item Type: | Article |
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Additional Information: | Preprint of published article. The original publication is available at www.springerlink.com. Research supported by the Claude Shannon Institute, Science Foundation Ireland Grant 06/MI/006 and the Irish Research Council for Science, Engineering and Technology |
Keywords: | almost perfect nonlinear; APN; automorphism group; CCZ-equivalence; EA-equivalence; Gold function; |
Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
Item ID: | 2690 |
Identification Number: | DOI: 10.1007/s10623-010-9475-8 |
Depositing User: | Hamilton Editor |
Date Deposited: | 01 Sep 2011 11:27 |
Journal or Publication Title: | Designs, Codes and Cryptography |
Publisher: | Springer |
Refereed: | No |
Funders: | Science Foundation Ireland, Irish Research Council for Science, Engineering and Technology |
Related URLs: | |
URI: | https://mural.maynoothuniversity.ie/id/eprint/2690 |
Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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