A new large class of functions not APN infinitely often
Florian Caullery
TL;DR
This paper proves that certain degree-4e vectorial Boolean functions cannot be APN infinitely often, advancing the understanding of the conjecture by Aubry, McGuire, and Rodier.
Contribution
It establishes a new class of functions that are not APN infinitely often, providing a significant step toward resolving the conjecture.
Findings
No vectorial Boolean function of degree 4e with certain conditions is APN infinitely often
Progress towards the conjecture of Aubry, McGuire, and Rodier
Advances understanding of the limitations of APN functions over field extensions
Abstract
In this paper, we show that there is no vectorial Boolean function of degree 4e, with e satisfaying certain conditions, which is APN over infinitely many extensions of its field of definition. It is a new step in the proof of the conjecture of Aubry, McGuire and Rodier
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Taxonomy
TopicsCoding theory and cryptography · Limits and Structures in Graph Theory · Polynomial and algebraic computation