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Introducing a new connection between the entries of MDS matrices constructed by generalized Cauchy matrices in GF(2q)
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Introducing a new connection between the entries of MDS matrices constructed by generalized Cauchy matrices in GF(2q)
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Journal Article
Introducing a new connection between the entries of MDS matrices constructed by generalized Cauchy matrices in GF(2q)
2023
Overview
Applying the maximum separable distance (MDS) matrices is one of the most common approaches to meet diffusion layer in modern block ciphers. Using Cauchy and extensions of Cauchy matrices are classical methods to generate MDS matrices. In this paper, using generalized Cauchy matrices, an approach to construct MDS matrices is proposed so that if
A
is an MDS matrix constructed with the proposed approach and
B
is a
3
×
3
sub-matrix of
A
, then interesting connections between the entries of
B
are introduced. More precisely, every element of the matrix
B
can be uniquely determined by eight other entries of
B
. Moreover, using generalized Cauchy matrices and also applying the proposed approach, some common forms of MDS matrices such as Hadamard, circulant and MDS matrices with maximum entries equal to the unit element, have been investigated.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
