Open AccessGeneralisation of Hadamard matrix to generate involutory MDS matrices for lightweight cryptography
Author(s) -
Pehlivanoğlu Meltem Kurt,
Sakallı Muharrem Tolga,
Akleylek Sedat,
Duru Nevcihan,
Rijmen Vincent
Publication year - 2018
Publication title -
iet information security
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 34
eISSN - 1751-8717
pISSN - 1751-8709
DOI - 10.1049/iet-ifs.2017.0156
Subject(s) - complex hadamard matrix , hadamard transform , involutory matrix , mathematics , hadamard matrix , matrix (chemical analysis) , context (archaeology) , hadamard product , hadamard's maximal determinant problem , arithmetic , algebra over a field , discrete mathematics , pure mathematics , symmetric matrix , square matrix , physics , mathematical analysis , paleontology , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material , biology
In this study, the authors generalise Hadamard matrix overF2 mand propose a new form of Hadamard matrix, which they call generalised Hadamard (GHadamard) matrix. Then, they focus on generating lightweight (involutory) maximum distance separable (MDS) matrices. They also extend this idea to any k × k matrix form, where k is not necessarily a power of 2. The new matrix form, GHadamard matrix, is used to generate new 4 × 4 involutory MDS matrices overF2 4andF2 8, and 8 × 8 involutory/non‐involutory MDS matrices overF2 4by considering the minimum exclusive OR (XOR) count, which is a metric defined to estimate the hardware implementation cost. In this context, they improve the best‐known results of XOR counts for 8 × 8 involutory/non‐involutory MDS matrices overF2 4.