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

2019/05/30 by Lilya Budaghyan, Nikolay Kaleyski, Budaghyan, Lilya +7
Computer Science · Medicine · #Coding theory and cryptography #Quantum-Dot Cellular Automata #Cancer Mechanisms and Therapy

paper · pdf · doi:10.48550/arxiv.1905.13025

Abstract

In this paper we define a notion of partial APNness and find various\ncharacterizations and constructions of classes of functions satisfying this\ncondition. We connect this notion to the known conjecture that APN functions\nmodified at a point cannot remain APN. In the second part of the paper, we find\nconditions for some transformations not to be partially APN, and in the\nprocess, we find classes of functions that are never APN for infinitely many\nextensions of the prime field F₂, extending some earlier results of Leander\nand Rodier.\n

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