Darrion Thornburgh

activity

20242026

collaborators

4 papers

math.CO2026

Resolving a conjecture on quadratic APN functions and a new quadratic $(n, n)$ -function associated to crooked functions

Claude Carlet, Darrion Thornburgh

We say an $(n, n)$ -function $F : F_{2}^{n} \to F_{2}^{n}$ is a crooked function if for any nonzero $a \in F_{2}^{n}$ , the image of $D_{a} F (x) = F (x) + F (x + a)$ is an af…

math.CO2025

On lower bounds for the distances between APN functions

Maria Mihaila, Darrion Thornburgh

Whether two distinct APN functions can have a Hamming distance of $1$ remains an open problem. In 2020, L. Budaghyan et al. introduced a new CCZ-invariant $Π_{F}$ which can be used t…

math.CO2025

On generalizing cryptographic results to Sidon sets in $F_{2}^{n}$

Darrion Thornburgh

A Sidon set $S$ in $F_{2}^{n}$ is a set such that $x + y = z + w$ has no solutions $x, y, z, w \in S$ with $x, y, z, w$ all distinct. In this paper, we prove various results on Sidon sets…

math.CO2024

Uniform exclude distributions of Sidon sets

Darrion Thornburgh

A Sidon set $S$ in $F_{2}^{n}$ is a set such that the pairwise sums of distinct points are all distinct. The exclude points of a Sidon set $S$ are the sums of three distinct p…

Resolving a conjecture on quadratic APN functions and a new quadratic (n,n)-function associated to crooked functions

On lower bounds for the distances between APN functions

On generalizing cryptographic results to Sidon sets in F2n​

Uniform exclude distributions of Sidon sets

Resolving a conjecture on quadratic APN functions and a new quadratic $(n, n)$ -function associated to crooked functions

On generalizing cryptographic results to Sidon sets in $F_{2}^{n}$