A New Algorithm for Computing Branch Number of Non-Singular Matrices Over Finite Fields

Document Type

Conference Article

Publication Title

Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics

Abstract

The notion of branch number of a linear transformation is crucial for both linear and differential cryptanalysis. The number of non-zero elements in a state difference or linear mask directly correlates with the active S-Boxes. The differential or linear branch number indicates the minimum number of active S-Boxes in two consecutive rounds of an SPN cipher, specifically for differential or linear cryptanalysis, respectively. This paper presents a new algorithm for computing the branch number of non-singular matrices over finite fields. The algorithm is based on the existing classical method but demonstrates improved computational complexity compared to its predecessor. We conduct a comparative study of the proposed algorithm and the classical approach, providing an analytical estimation of the algorithm’s complexity. Our analysis reveals that the computational complexity of our algorithm is the square root of that of the classical approach.

First Page

187

Last Page

205

DOI

10.1007/978-3-031-71073-5_9

Publication Date

1-1-2024

Comments

Open Access; Green Open Access

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