[Resource Topic] 2023/448: Generalized Inverse Matrix Construction for Code Based Cryptography

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Generalized Inverse Matrix Construction for Code Based Cryptography

Authors: Farshid Haidary Makoui, T. Aaron Gulliver


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^{k\times(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.

ePrint: https://eprint.iacr.org/2023/448

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