2021/12/16 by Maximilien Gadouleau, Gadouleau, Maximilien, Luca Mariot +3 · 1 citation
Computer Science · Mathematics · Medicine · #Bent function #Bent molecular geometry #Boolean function #Cancer Mechanisms and Therapy #Class (philosophy) #Coding theory and cryptography #Combinatorics #Combinatorics (math.CO) #Computer science #Coprime integers #Cryptography and Security (cs.CR) #Degree (music) #Discrete mathematics #FOS: Computer and information sciences #FOS: Mathematics #Function (biology) #Intersection (aeronautics) #Linear subspace #Mathematics #Peptidase Inhibition and Analysis #Physics #Prime (order theory) #Pure mathematics #Rank (graph theory) #cs.CR #math.CO
paper · pdf · doi:10.48550/arxiv.2112.08705
Completely revised version of "Bent functions from Cellular Automata" published in the Cryptology ePrint Archive. The construction here is described with linear recurring sequences instead of cellular automata, with new results. The original version in the ePrint archive is a standalone work discussing the connections between CA, Hadamard matrices, bent functions and orthogonal arrays
arxiv created 2021/12/16 · openalex publication_date 2021/12/16 · arxiv updated 2021/12/17 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/06
We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if their feedback polynomials are relatively prime. Then, we characterize the appropriate parameters for a family of pairwise coprime polynomials to generate a partial spread required for the support of a bent function, showing that such families exist if and only if the degrees of the underlying polynomials is either 1 or 2. We then count the resulting sets of polynomials and prove that for degree 1, our LRS construction coincides with the Desarguesian partial spread. Finally, we perform a computer search of all PS- and PS+ bent functions of n=8 variables generated by our construction and compute their 2-ranks. The results show that many of these functions defined by polynomials of degree b=2 are not EA-equivalent to any Maiorana-McFarland or Desarguesian partial spread function.