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Generalization of a class of APN binomials to Gold-like functions

Davidova, Diana; Kaleyski, Nikolay Stoyanov
Journal article, Peer reviewed
Accepted version
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URI
https://hdl.handle.net/11250/2988041
Date
2021
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  • Department of Informatics [740]
  • Registrations from Cristin [5237]
Original version
Lecture Notes in Computer Science (LNCS). 2021, 12542, 195-206   10.1007/978-3-030-68869-1_11
Abstract
In 2008 Budaghyan, Carlet and Leander generalized a known instance of an APN function over the finite field F212 and constructed two new infinite families of APN binomials over the finite field F2n , one for n divisible by 3, and one for n divisible by 4. By relaxing conditions, the family of APN binomials for n divisible by 3 was generalized to a family of differentially 2t -uniform functions in 2012 by Bracken, Tan and Tan; in this sense, the binomials behave in the same way as the Gold functions. In this paper, we show that when relaxing conditions on the APN binomials for n divisible by 4, they also behave in the same way as the Gold function x2s+1 (with s and n not necessarily coprime). As a counterexample, we also show that a family of APN quadrinomials obtained as a generalization of a known APN instance over F210 cannot be generalized to functions with 2t -to-1 derivatives by relaxing conditions in a similar way.
Publisher
Springer
Journal
Lecture Notes in Computer Science (LNCS)
Copyright
Copyright 2021 Springer

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