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Cryptography and Communications
Published in: Cryptography and Communications 2/2015

01-06-2015

Cryptographically significant MDS matrices based on circulant and circulant-like matrices for lightweight applications

Authors: Kishan Chand Gupta, Indranil Ghosh Ray

Published in: Cryptography and Communications | Issue 2/2015

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Abstract

MDS matrices incorporate diffusion layers in block ciphers and hash functions. MDS matrices are in general not sparse and have a large description and thus induce costly implementations both in hardware and software. It is also nontrivial to find MDS matrices which could be used in lightweight cryptography. In the AES MixColumn operation, a circulant MDS matrix is used which is efficient as its elements are of low hamming weights, but no general constructions and study of MDS matrices from d×d circulant matrices for arbitrary d is available in the literature. In a SAC 2004 paper, Junod et al. constructed a new class of efficient matrices whose submatrices were circulant matrices and they coined the term circulating-like matrices for these new class of matrices. We call these matrices as Type-I circulant-like matrices. In this paper we introduce a new type of circulant-like matrices which are involutory by construction and we call them Type-II circulant-like matrices.
We study the MDS properties of d×d circulant, Type-I and Type-II circulant-like matrices and construct new and efficient MDS matrices which are suitable for lightweight cryptography for d up to 8. We also consider orthogonal and involutory properties of such matrices and study the construction of efficient MDS matrices whose inverses are also efficient. We explore some interesting and useful properties of circulant, Type-I and Type-II circulant-like matrices which are prevalent in many parts of mathematics and computer science.
previous article Repeated-root constacyclic codes of length ℓ t p s and their dual codes

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Appendix
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Metadata
Title
Cryptographically significant MDS matrices based on circulant and circulant-like matrices for lightweight applications
Authors
Kishan Chand Gupta
Indranil Ghosh Ray
Publication date
01-06-2015
Publisher
Springer US
Published in
Cryptography and Communications / Issue 2/2015
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI
https://doi.org/10.1007/s12095-014-0116-3

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