Paper 2017/368

Analysis of Toeplitz MDS Matrices

Sumanta Sarkar and Habeeb Syed

Abstract

This work considers the problem of constructing efficient MDS matrices over the field $\F_{2^m}$. Efficiency is measured by the metric XOR count which was introduced by Khoo et al. in CHES 2014. Recently Sarkar and Syed (ToSC Vol. 1, 2016) have shown the existence of $4\times 4$ Toeplitz MDS matrices with optimal XOR counts. In this paper, we present some characterizations of Toeplitz matrices in light of MDS property. Our study leads to improving the known bounds of XOR counts of $8\times 8$ MDS matrices by obtaining Toeplitz MDS matrices with lower XOR counts over $\F_{2^4}$ and $\F_{2^8}$.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Published elsewhere. ACISP 2017
Keywords
Toeplitz matrixMDS matrixXOR countlightweight block cipherdiffusion layer
Contact author(s)
sumanta sarkar @ gmail com
History
2017-04-28: received
Short URL
https://ia.cr/2017/368
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2017/368,
      author = {Sumanta Sarkar and Habeeb Syed},
      title = {Analysis of Toeplitz {MDS} Matrices},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/368},
      year = {2017},
      url = {https://eprint.iacr.org/2017/368}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.