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Title:
Two new infinite families of APN functions in triviariate form
Authors: Kangquan Li, Nikolay Kaleyski
Abstract:We present two infinite families of APN functions in triviariate form over finite fields of the form \mathbb{F}_{2^{3m}}. We show that the functions from both families are permutations when m is odd, and are 3-to-1 functions when m is even. In particular, our functions are AB permutations for m odd. Furthermore, we observe that for m = 3, i.e. for \mathbb{F}_{2^9}, the functions from our families are CCZ-equivalent to the two bijective sporadic APN instances discovered by Beierle and Leander.
ePrint: https://eprint.iacr.org/2022/1522
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