Partially APN Boolean functions and classes of functions that are not APN infinitely often

Budaghyan, Lilya; Kaleyski, Nikolay Stoyanov; Kwon, Soonhak; Riera, Constanza Susana; Stănică, Pantelimon
Peer reviewed, Journal article
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https://hdl.handle.net/11250/2647198
Date
2019
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Original version
Budaghyan, L., Kaleyski, N. S., Kwon, S., Riera, C., & Stănică, P. (2019). Partially APN Boolean functions and classes of functions that are not APN infinitely often. Cryptography and Communications, 2019.   10.1007/s12095-019-00372-8
Abstract
In this paper we define a notion of partial APNness and find various characterizations and constructions of classes of functions satisfying this condition. We connect this notion to the known conjecture that APN functions modified at a point cannot remain APN. In the second part of the paper, we find conditions for some transformations not to be partially APN, and in the process, we find classes of functions that are never APN for infinitely many extensions of the prime field F2, extending some earlier results of Leander and Rodier.
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This is a pre-print of an article published in Cryptography and Communications. The final authenticated version is available online at: https://doi.org/10.1007/s12095-019-00372-8
Publisher
Springer
Journal
Cryptography and Communications