Functions of degree 4e that are not APN infinitely often

International audienceWe prove a necessary condition for some polynomials of degree 4e (e an odd number) to be APN over F q n for large n, and we investigate the polynomials f of degree 12

A new large class of functions not APN infinitely often

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 Rodie

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

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 \F_2, extending some earlier results of Leander and Rodier.Comment: 24 pages; to appear in Cryptography and Communication

Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents

International audienceWe prove a necessary condition for some polynomials of Gold and Kasami degree to be APN over F q n for large n

Some More Functions That Are Not APN Infinitely Often. The Case of Kasami exponents

We prove a necessary condition for some polynomials of Kasami degree to be APN over F_{q^n} for large n.Comment: 1