In a recent work, Beierle, Brinkmann and Leander presented a recursive tree search for
finding APN permutations with linear self-equivalences in small dimensions. In this paper …

Almost perfect nonlinear functions possess optimal resistance to differential cryptanalysis
and are widely studied. Most known APN functions are defined using their representation as …

All almost perfect nonlinear (APN) permutations that we know to date admit a special kind of
linear self-equivalence, ie, there exists a permutation G in their CCZ-equivalence class and …

Finding new (up to CCZ-equivalence) constructions of APN functions is one of the important
but difficult topics in the study of cryptographic functions. Up to now, only 6 infinite families of …

Almost perfect nonlinear functions possess the optimal resistance to the differential
cryptanalysis and are widely studied. Most known APN functions are obtained as functions …

In this work, we study functions that can be obtained by restricting a vectorial Boolean
function F: F 2 n→ F 2 n to an affine hyperplane of dimension n-1 and then projecting the …

We describe how any function over a finite field $\mathbb {F} _ {p^ n} $ can be represented
in terms of the values of its derivatives. In particular, we observe that a function of algebraic …

Yu et al. described an algorithm for conducting computational searches for quadratic APN
functions over the finite field $\mathbb {F} _ {2^ n} $, and used this algorithm to give a …

APN functions offer optimal resistance to differential attacks and are instrumental in the
design of block ciphers in cryptography. While finding APN functions is very difficult in …

We investigate how far the approach of searching for APN functions by expanding their
univariate representation can be pushed. We present some theoretical tricks that can be …