Paper 2022/1522

Two new infinite families of APN functions in trivariate form

Kangquan Li, National University of Defense Technology, China
Nikolay Kaleyski, University of Bergen
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. We also perform an exhaustive computational search for quadratic APN functions with binary coefficients in trivariate form over $\mathbb{F}_{2^{3m}}$ with $m \le 5$ and report on the results.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint.
Keywords
APN AB permutation differential uniformity trivariate
Contact author(s)
likangquan11 @ nudt edu cn
nikolay kaleyski @ gmail com
History
2022-11-28: revised
2022-11-03: received
See all versions
Short URL
https://ia.cr/2022/1522
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2022/1522,
      author = {Kangquan Li and Nikolay Kaleyski},
      title = {Two new infinite families of {APN} functions in trivariate form},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/1522},
      year = {2022},
      url = {https://eprint.iacr.org/2022/1522}
}
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