Applications of design theory for the constructions of MDS matrices for lightweight cryptography

Autor: Gupta Kishan Chand, Pandey Sumit Kumar, Ray Indranil Ghosh
Jazyk: angličtina
Rok vydání: 2017
Předmět:
Zdroj: Journal of Mathematical Cryptology, Vol 11, Iss 2, Pp 85-116 (2017)
Druh dokumentu: article
ISSN: 1862-2976
1862-2984
DOI: 10.1515/jmc-2016-0013
Popis: In this paper, we observe simple yet subtle interconnections among design theory, coding theory and cryptography. Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is nontrivial to find MDS matrices which could be used in lightweight cryptography. In the SAC 2004 paper [12], Junod and Vaudenay considered bi-regular matrices which are useful objects to build MDS matrices. Bi-regular matrices are those matrices all of whose entries are nonzero and all of whose 2×2{2\times 2} submatrices are nonsingular. Therefore MDS matrices are bi-regular matrices, but the converse is not true. They proposed the constructions of efficient MDS matrices by studying the two major aspects of a d×d{d\times d} bi-regular matrix M, namely v1⁢(M){v_{1}(M)}, i.e. the number of occurrences of 1 in M, and c1⁢(M){c_{1}(M)}, i.e. the number of distinct elements in M other than 1. They calculated the maximum number of ones that can occur in a d×d{d\times d} bi-regular matrices, i.e. v1d,d{v_{1}^{d,d}} for d up to 8, but with their approach, finding v1d,d{v_{1}^{d,d}} for d≥9{d\geq 9} seems difficult.
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