Open AccessLightweight Diffusion Layer: Importance of Toeplitz Matrices
Author(s) -
Sumanta Sarkar,
Habeeb Syed
Publication year - 2016
Publication title -
iacr transaction on symmetric cryptology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.715
H-Index - 10
ISSN - 2519-173X
DOI - 10.46586/tosc.v2016.i1.95-113
Subject(s) - toeplitz matrix , mathematics , matrix (chemical analysis) , metric (unit) , diffusion , pure mathematics , discrete mathematics , algebra over a field , physics , chemistry , engineering , chromatography , thermodynamics , operations management
MDS matrices are used as building blocks of diffusion layers in block ciphers, and XOR count is a metric that estimates the hardware implementation cost. In this paper we report the minimum value of XOR counts of 4 × 4 MDS matrices over F24 and F28 , respectively. We give theoretical constructions of Toeplitz MDS matrices and show that they achieve the minimum XOR count. We also prove that Toeplitz matrices cannot be both MDS and involutory. Further we give theoretical constructions of 4 × 4 involutory MDS matrices over F24 and F28 that have the best known XOR counts so far: for F24 our construction gives an involutory MDS matrix that actually improves the existing lower bound of XOR count, whereas for F28 , it meets the known lower bound.