Equivalences of quadratic APN functions

نویسنده

  • Satoshi Yoshiara
چکیده

The following conjecture due to Y. Edel is affirmatively solved: two quadratic APN (almost perfect nonlinear) functions are CCZ-equivalent if and only if they are extended affine equivalent.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A matrix approach for constructing quadratic APN functions

We find a one to one correspondence between quadratic APN functions without linear and constant terms and a special kind of matrices (We call such matrices as QAMs). Based on the nice mathematical structures of the QAMs, we have developed efficient algorithms to construct quadratic APN functions. On F27 , we have found more than 470 classes of new CCZ-inequivalent quadratic APN functions, which...

متن کامل

Some Results on the Known Classes of Quadratic APN Functions

In this paper, we determine theWalsh spectra of three classes of quadratic APN functions and we prove that the class of quadratic trinomial APN functions constructed by Göloğlu is affine equivalent to Gold functions.

متن کامل

Quadratic Binomial APN Functions and Absolutely Irreducible Polynomials

We show that many quadratic binomial functions of the form cx i +2 j + dx u +2 v (c, d ∈ GF (2m)) are not APN infinitely often. This is of interest in the light of recent discoveries of new families of quadratic binomial APN functions. The proof uses the Weil bound from algebraic geometry.

متن کامل

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. Ou...

متن کامل

On the Fourier spectra of the infinite families of quadratic APN functions

It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the Fourier spectrum of a function and the APN property. In this article we compute the Fourier spectrum of the quadranomial family of APN functions from [5]. W...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012