## CryptoDB

### Paper: Lightweight Diffusion Layer: Importance of Toeplitz Matrices

Authors: Sumanta Sarkar , TCS Innovation Labs, Hyderabad Habeeb Syed , TCS Innovation Labs, Hyderabad DOI: 10.13154/tosc.v2016.i1.95-113 URL: http://tosc.iacr.org/index.php/ToSC/article/view/537 Search ePrint Search Google 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.
##### BibTeX
@article{tosc-2016-28123,
title={Lightweight Diffusion Layer: Importance of Toeplitz Matrices},
journal={IACR Trans. Symmetric Cryptol.},
publisher={Ruhr-Universität Bochum},
volume={2016, Issue 1},
pages={95-113},
url={http://tosc.iacr.org/index.php/ToSC/article/view/537},
doi={10.13154/tosc.v2016.i1.95-113},
author={Sumanta Sarkar and Habeeb Syed},
year=2016
}