Two new infinite families of APN functions in trivariate form

K Li, N Kaleyski - IEEE Transactions on Information Theory, 2023 - ieeexplore.ieee.org
We present two infinite families of APN functions in trivariate form over finite fields of the
form. We show that the functions from both families are permutations when is odd, and are 3 …

On a conjecture on APN permutations

D Bartoli, M Timpanella - Cryptography and Communications, 2022 - Springer
The single trivariate representation proposed in [C. Beierle, C. Carlet, G. Leander, L. Perrin,
A Further Study of Quadratic APN Permutations in Dimension Nine, arXiv: 2104.08008] of …

Invertible Quadratic Non-Linear Functions over via Multiple Local Maps

G Giordani, L Grassi, S Onofri, M Pedicini - Cryptology ePrint Archive, 2023 - eprint.iacr.org
The construction of invertible non-linear layers over $\mathbb F_p^ n $ that minimize the
multiplicative cost is crucial for the design of symmetric primitives targeting Multi Party …

Invertible Quadratic Non-linear Functions over  via Multiple Local Maps

G Giordani, L Grassi, S Onofri, M Pedicini - International Conference on …, 2023 - Springer
The construction of invertible non-linear layers over F pn that minimize the multiplicative cost
is crucial for the design of symmetric primitives targeting Multi Party Computation (MPC) …

New results on PcN and APcN polynomials over finite fields

Z Zha, L Hu - Finite Fields and Their Applications, 2024 - Elsevier
Permutation polynomials with low c-differential uniformity have important applications in
cryptography and combinatorial design. In this paper, we investigate perfect c-nonlinear …

Constructing rotatable permutations of with -homogeneous functions

Y Chi, K Li, L Qu - arXiv preprint arXiv:2401.17094, 2024 - arxiv.org
In the literature, there are many results about permutation polynomials over finite fields.
However, very few permutations of vector spaces are constructed although it has been …

Exceptional crooked functions

D Bartoli, M Calderini, M Timpanella - Finite Fields and Their Applications, 2022 - Elsevier
Crooked functions are combinatorial objects of great interest. It is already known that the
only monomial and binomial crooked functions are quadratic. In this paper, we investigate …

A proof of a conjecture on trivariate permutations

D Bartoli, M Pal, P Stanica, T Toccotelli - arXiv preprint arXiv:2410.23097, 2024 - arxiv.org
In this note we show (for a large enough dimension of the underlying field) a conjecture of
[C. Beierle, C. Carlet, G. Leander, L. Perrin,{\em A further study of quadratic APN …

Construction of APN permutations via Walsh zero spaces

B Chase, P Lisoněk - Cryptography and Communications, 2022 - Springer
A Walsh zero space (WZ space) for f: F 2 n→ F 2 n is an n-dimensional vector subspace of F
2 n× F 2 n whose all nonzero elements are Walsh zeros of f. We provide several theoretical …

Constructions of APN permutations

B Chase - 2021 - summit.sfu.ca
APN functions defined on finite fields of characteristic two provide the best protection against
differential cryptanalysis. They are used extensively in modern symmetric block ciphers. It is …