Parallel Algorithm for Finding Inverse of a Matrix and its Application in Message Sharing (Coding Theory)

Saraf, Shruti; Dhingra, Swati; Pinheiro, G.

doi:10.5120/ijca2016908569

“…The generalized inverse of a systematic binary matrix is used for decoding in all applications of error-correcting codes including digital communication [1], navigation signals [2], data storage systems [3] and coding theory [4] in cryptography. Generalized inverse matrices can be obtained using Gauss-Jordan elimination [5] and Moore-Penrose pseudoinverse (MPP) techniques [6] [7].…”

Section: Introductionmentioning

confidence: 99%

Generalized Inverse Matrix Construction for Code Based Cryptography

Makoui¹,

Gulliver²

2023

Preprint

0

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<p>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.</p>

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“…The generalized inverse of a systematic binary matrix is used for decoding in all applications of error-correcting codes including digital communication [1], navigation signals [2], data storage systems [3] and coding theory [4] in cryptography. Generalized inverse matrices can be obtained using Gauss-Jordan elimination [5] and Moore-Penrose pseudoinverse (MPP) techniques [6] [7].…”

Section: Introductionmentioning

confidence: 99%

Generalized Inverse Matrix Construction for Code Based Cryptography

Makoui¹,

Gulliver²

2023

Preprint

0

View full text Add to dashboard Cite

<p>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.</p>

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Inverse matrices with applications in public-key cryptography

Haidary Makoui,

Gulliver

2024

Journal of Algorithms & Computational Technology

1

0

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The applications of non-square binary matrices span many domains including mathematics, error-correction coding, machine learning, data storage, navigation signals, and cryptography. In particular, they are employed in the McEliece and Niederreiter public-key cryptosystems. For the parity check matrix of these cryptosystems, a systematic non-square binary matrix [Formula: see text] with dimensions [Formula: see text], [Formula: see text], [Formula: see text], there exist [Formula: see text] distinct inverse matrices. This article presents an algorithm to generate these matrices as well as a method to construct a random inverse matrix. Then it is extended to non-square matrices in arbitrary fields. This overcomes the limitations of the Moore-Penrose and Gauss-Jordan methods. The application to public-key cryptography is also discussed.

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Parallel Algorithm for Finding Inverse of a Matrix and its Application in Message Sharing (Coding Theory)

Cited by 3 publications

References 5 publications

Generalized Inverse Matrix Construction for Code Based Cryptography

Generalized Inverse Matrix Construction for Code Based Cryptography

Generalized Inverse Matrix Construction for Code Based Cryptography

Inverse matrices with applications in public-key cryptography

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