New semifields, PN and APN functions

New semifields, PN and APN functions

Constructing new APN functions from known ones

We present a method for constructing new quadratic APN functions from known ones. Applying this method to the Gold power functions we construct an APN function x3 + tr(x9) over F2n . It is proven that in general this function is CCZinequivalent to the Gold functions (and therefore EA-inequivalent to power functions), to the inverse and Dobbertin mappings, and in the case n = 7 it is CCZinequiva...

Planar Functions and Commutative Semifields

This paper gives a short survey on planar functions and commutative semifields and considers a possible extension of CCZ-equivalence which is the most general known equivalence relation of functions preserving the planar property. 1. PN and APN functions Let p be any prime number and n any positive integer. A function F from the field Fpn to itself is called planar if all the equations F (x+ a)...

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 Rodier. Vectorial Boolean function and Almost Perfect Non-linear functions and Algebraic surface and CCZ equivalence

On the Fourier Spectra of New APN Functions

Almost perfect nonlinear (APN) functions on F2n are functions achieving the lowest possible differential uniformity. All APN functions discovered until now are either power or quadratic ones, except for one sporadic multinomial nonquadratic example on F26 due to Edel and Pott. It is well known that certain binary codes with good properties can be obtained from APN functions, and determining the...