8 citations · 8 across the 5 of their papers we have counts for
5 papers
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…
Normality of 8-Bit Bent Function
Valérie Gillot, Philippe Langevin, Alexandr Polujan
Bent functions are Boolean functions in an even number of variables that are indicators of Hadamard difference sets in elementary abelian 2-groups. A bent function in m variables i…
The combinatorial structure and value distributions of plateaued functions
Lukas Kölsch, Alexandr Polujan
We study combinatorial properties of plateaued functions . All quadratic functions, bent functions and most known APN functions…
On the normality of Boolean quartics
Valérie Gillot, Philippe Langevin, Alexandr Polujan
In the BFA 2023 conference paper, A. Polujan, L. Mariot and S. Picek exhibited the first example of a non-normal but weakly normal bent function in dimension 8. In this note, we pr…
Value Distributions of Perfect Nonlinear Functions
Lukas Kölsch, Alexandr Polujan
In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we deve…