On the Equivalence of Quadratic APN Functions

Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to an APN Gold function if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2^n where n = 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function.Comment: 13 p

A Few More Quadratic APN Functions

We present two infinite families of APN functions on GF(2n) where n is divisible by 3 but not 9. Our families contain two already known families as special cases. We also discuss the inequivalence proof (by computation) which shows that these functions are new

A Few More Quadratic APN Functions

We present two infinite families of APN functions on GF(2n) where n is divisible by 3 but not 9. Our families contain two already known families as special cases. We also discuss the inequivalence proof (by computation) which shows that these functions are new

A Few More Quadratic APN Functions

We present two infinite families of APN functions on GF(2n) where n is divisible by 3 but not 9. Our families contain two already known families as special cases. We also discuss the inequivalence proof (by computation) which shows that these functions are new

A Few More Quadratic APN Functions

We present two infinite families of APN functions on GF(2n) where n is divisible by 3 but not 9. Our families contain two already known families as special cases. We also discuss the inequivalence proof (by computation) which shows that these functions are new

Fourier Spectra of Binomial APN Functions

In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis. Another consequence is that certain error-correcting codes related to these functions have the same weight distribution as the 2-error-correcting BCH code. Furthermore, for field extensions of F2 of odd degree, our results provide an alternative proof of the APN property of the functions