June 1, 2023


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Generalized Inverse Matrix Construction for Code Based Cryptography

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 $(n-k) times k$ matrix $H$, $n > k$, has $2^{ktimes(n-k)}$ 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 methods. A random generalized inverse matrix construction method is given which has a lower execution time than the Gauss-Jordan elimination and Moore-Penrose approaches.