Work

Permutation equivalence of $ k $ -rotation symmetric monomial Boolean functions

Year: 2026

Type: article

Abstract: Two Boolean functions $ f({\mathbf x}) $ and $ g({\mathbf x}) $ are affine equivalent if there exist a nonsingular binary matrix $ A $ and a binary vector $ {\mathbf b} $ that satisfy the relation $ f(A{\mathbf x}+{\mathbf b}) = g({\mathbf x}) $. Important concepts in cryptography, such as balancedness and nonlinearity, are affine invariants. In this paper, we study the affine equivalence of $ k $-rotation symmetric monomial Boolean functions obtained from the action of permutation groups. We construct affine equivalence classes of $ k $-rotation symmetric monomial Boolean functions using $ k $-rotation preserving permutations. Furthermore, we provide bounds for the number of elements in each equivalence class.

Source: Advances in Mathematics of Communications

DOI: 10.3934/amc.2026062

Authors: José E. Calderón-Gómez, Luis A. Medina, Carlos A. Molina-Salazar

Institutions: University of Puerto Rico-Mayaguez, University of Puerto Rico System, University of Puerto Rico at Arecibo

Language: English

Topic: Coding theory and cryptography

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Puerto Rico Science, Technology and Research Trust

Award: G7320771615