René Rodríguez-Aldama

University of Primorska | UP · Department of Mathematics

This article provides a rigorous mathematical treatment of generalized (GNI) and closed-loop invariants (CLI), which extend the standard notion of nonlinear invariants used in the cryptanalysis of block ciphers. We first introduce the concept of an active cycle set, which is useful for defining standard invariants of concatenated S-boxes. We also p...

Minimal codes are characterized by the property that none of the codewords is covered by some other linearly independent codeword. We first show that the use of a bent function g in the so-called direct sum of Boolean functions h(x,y)=f(x)+g(y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{...

Minimal binary linear codes are a special class of binary codes with important applications in secret sharing and secure two-party computation. These codes are characterized by the property that none of the nonzero codewords is covered by any other codeword. Denoting by \(w_{{\min \limits }}\) and \(w_{{\max \limits }}\) the minimum and maximum wei...

Minimal linear codes form a special class of linear codes that have important applications in secret sharing and secure two-party computation. These codes are characterized by the property that linearly independent codewords do not cover each other. Denoting by wmin and wmax the minimum and maximum weights of a binary code, respectively, such codes...