On Constructions of Involutory MDS Matrices

Gupta, Kishan Chand; Ray, Indranil Ghosh

doi:10.1007/978-3-642-38553-7_3

Cited by 34 publications

(25 citation statements)

References 18 publications

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“…Definition 2.1. [21] Let F be a finite field and p and q be two integers. Let x → M × x be a mapping from F p to F q defined by the q × p matrix M .…”

Section: Definition and Preliminariesmentioning

confidence: 99%

“…Application of Cauchy matrices for constructing MDS codes are widely available in literature [13,21,45,46,51,52,63,69]. Youssef et.…”

Section: Constructing Mds Matrices From Cauchy Matricesmentioning

confidence: 99%

“…[46] used triangular array to construct MDS codes, which is related with Cauchy matrices [46,51]. We will mainly discuss [13,21,46,51,52,69] in this section.…”

Section: Constructing Mds Matrices From Cauchy Matricesmentioning

confidence: 99%

“…From Corollary 6, a n × n matrix constructed using Lemma 3.2 has at least n distinct elements. In [21], authors constructed n × n MDS matrices with exactly n distinct elements. It has two-fold advantage.…”

Section: Corollary 6 [21 Corollary 1]mentioning

confidence: 99%

“…Since these elements are nothing but the multiplicative inverse of elements of l + G in F 2 r , the matrix A has exactly n different elements. In [21], authors provided a sufficient condition (Lemma 3.4 of this paper) for a Cauchy MDS matrix to be a compact Cauchy but did not discuss about the converse part. Later in [13], authors provided a necessary and sufficient condition for the Cauchy matrix of order n to have exactly n distinct elements.…”

Section: Corollary 6 [21 Corollary 1]mentioning

confidence: 99%

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Cryptographically significant mds matrices over finite fields: A brief survey and some generalized results

Gupta¹,

Pandey²,

Ray³

et al. 2019

Advances in Mathematics of Communications

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A matrix is MDS or super-regular if and only if every square submatrices of it are nonsingular. MDS matrices provide perfect diffusion in block ciphers and hash functions. In this paper we provide a brief survey on cryptographically significant MDS matrices-a first to the best of our knowledge. In addition to providing a summary of existing results, we make several contributions. We exhibit some deep and nontrivial interconnections between different constructions of MDS matrices. For example, we prove that all known Vandermonde constructions are basically equivalent to Cauchy constructions. We prove some folklore results which are used in MDS matrix literature. Wherever possible, we provide some simpler alternative proofs. We do not discuss efficiency issues or hardware implementations; however, the theory accumulated and discussed here should provide an easy guide towards efficient implementations.

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“…Definition 2.1. [21] Let F be a finite field and p and q be two integers. Let x → M × x be a mapping from F p to F q defined by the q × p matrix M .…”

Section: Definition and Preliminariesmentioning

confidence: 99%

“…Application of Cauchy matrices for constructing MDS codes are widely available in literature [13,21,45,46,51,52,63,69]. Youssef et.…”

Section: Constructing Mds Matrices From Cauchy Matricesmentioning

confidence: 99%

“…[46] used triangular array to construct MDS codes, which is related with Cauchy matrices [46,51]. We will mainly discuss [13,21,46,51,52,69] in this section.…”

Section: Constructing Mds Matrices From Cauchy Matricesmentioning

confidence: 99%

Section: Corollary 6 [21 Corollary 1]mentioning

confidence: 99%

Section: Corollary 6 [21 Corollary 1]mentioning

confidence: 99%

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