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• #### Classification of quadratic APN functions with coefficients in F2 for dimensions up to 9 ﻿

(Journal article; Peer reviewed, 2020)
Almost perfect nonlinear (APN) and almost bent (AB) functions are integral components of modern block ciphers and play a fundamental role in symmetric cryptography. In this paper, we describe a procedure for searching for ...
• #### Deciding EA-equivalence via invariants ﻿

(Journal article; Peer reviewed, 2022)
We define a family of efficiently computable invariants for (n,m)-functions under EA-equivalence, and observe that, unlike the known invariants such as the differential spectrum, algebraic degree, and extended Walsh spectrum, ...
• #### Generalization of a class of APN binomials to Gold-like functions ﻿

(Journal article; Peer reviewed, 2021)
In 2008 Budaghyan, Carlet and Leander generalized a known instance of an APN function over the finite field F212 and constructed two new infinite families of APN binomials over the finite field F2n , one for n divisible ...
• #### Invariants for EA- and CCZ-equivalence of APN and AB functions ﻿

(Journal article; Peer reviewed, 2021)
An (n,m)-function is a mapping from ${\mathbb {F}_{2}^{n}}$ to ${\mathbb {F}_{2}^{m}}$. Such functions have numerous applications across mathematics and computer science, and in particular are used as building blocks ...
• #### A New Family of APN Quadrinomials ﻿

(Journal article; Peer reviewed, 2020)
The binomial B(x) = x 3 +βx 36 (where β is primitive in F 2 2) over F 2 10 is the first known example of an Almost Perfect Nonlinear (APN) function that is not CCZ-equivalent to a power function, and has remained unclassified ...
• #### On the behavior of some APN permutations under swapping points ﻿

(Journal article; Peer reviewed, 2022)
We define the pAPN-spectrum (which is a measure of how close a function is to being APN) of an (n, n)-function F and investigate how its size changes when two of the outputs of a given function F are swapped. We completely ...
• #### On the Distance Between APN Functions ﻿

(Journal article; Peer reviewed, 2020)
We investigate the differential properties of a vectorial Boolean function G obtained by modifying an APN function F . This generalizes previous constructions where a function is modified at a few points. We characterize ...
• #### Partially APN functions with APN-like polynomial representations ﻿

(Journal article; Peer reviewed, 2020)
In this paper we investigate several families of monomial functions with APN-like exponents that are not APN, but are partially 0-APN for infinitely many extensions of the binary field F2. We also investigate the differential ...
• #### Towards a deeper understanding of APN functions and related longstanding problems ﻿

(Doctoral thesis, 2021-08-24)
This dissertation is dedicated to the properties, construction and analysis of APN and AB functions. Being cryptographically optimal, these functions lack any general structure or patterns, which makes their study very ...