Paper 2023/519

Generalized Inverse Binary Matrix Construction with PKC Application

Abstract

The generalized inverses of systematic non-square binary matrices have applications in mathematics, channel coding and decoding, navigation signals, machine learning, data storage, and cryptography, such as the McEliece and Niederreiter public-key cryptosystems. A systematic non-square (n−k)×n matrix H, n > k, has 2 power k×(n−k) different generalized inverse matrices. This paper presents an algorithm for generating these matrices and compares it with two well-known methods, i.e. Gauss-Jordan elimination and Moore-Penrose. A random generalized inverse matrix construction method is given, which has a lower execution time than the Gauss-Jordan elimination and Moore-Penrose approaches. This paper also expands the novel idea to non-systematic non-square binary matrices and provides an application in public-key cryptosystems.