40 citations · 72 across the 10 of their papers we have counts for
11 papers
Linearity bounds for APN functions
Christof Beierle, Lukas Kölsch
For , let be almost perfect nonlinear and write . It is proven that the linearity of , i.e., the largest…
Millions of inequivalent quadratic APN functions in eight variables
Christof Beierle, Philippe Langevin, Gregor Leander +2
The only known example of an almost perfect nonlinear (APN) permutation in even dimension was obtained by applying CCZ-equivalence to a specific quadratic APN function in dimension…
A degree bound for planar functions
Christof Beierle, Tim Beyne
Using Stickelberger's theorem on Gauss sums, we show that if is a planar function on a finite field , then for all non-zero functions $G : \mathbb{F}_q \to \mathb…
On Matrix Algebras Isomorphic to Finite Fields and Planar Dembowski-Ostrom Monomials
Christof Beierle, Patrick Felke
Let be a prime and a positive integer. As the first main result, we present a deterministic algorithm for deciding whether the matrix algebra …
Generalized Almost Perfect Nonlinear Binomials and Trinomials Over Fields of Prime-Square Order
Christof Beierle
Let be a prime. We show that, for each integer with , there exists a generalized almost perfect nonlinear (GAPN) binomial or trinomial over $\mathbb…
Classification of Planar Monomials Over Finite Fields of Small Order
Christof Beierle, Patrick Felke
For all finite fields of order up to , we computationally prove that there are no planar monomials besides the ones already known.
Gold Functions and Switched Cube Functions Are Not 0-Extendable in Dimension
Christof Beierle, Claude Carlet
In the independent works by Kalgin and Idrisova and by Beierle, Leander and Perrin, it was observed that the Gold APN functions over give rise to a quadratic APN…
Trims and Extensions of Quadratic APN Functions
Christof Beierle, Gregor Leander, Léo Perrin
In this work, we study functions that can be obtained by restricting a vectorial Boolean function to an affine hyperplane of di…
A Further Study of Quadratic APN Permutations in Dimension Nine
Christof Beierle, Claude Carlet, Gregor Leander +1
Recently, Beierle and Leander found two new sporadic quadratic APN permutations in dimension 9. Up to EA-equivalence, we present a single trivariate representation of those two per…
New Instances of Quadratic APN Functions
Christof Beierle, Gregor Leander
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, we…
Linearly Self-Equivalent APN Permutations in Small Dimension
Christof Beierle, Marcus Brinkmann, Gregor Leander
All almost perfect nonlinear (APN) permutations that we know to date admit a special kind of linear self-equivalence, i.e., there exists a permutation in their CCZ-equivalence…