Paper 2016/119

Lightweight Multiplication in GF(2^n) with Applications to MDS Matrices

Christof Beierle, Thorsten Kranz, and Gregor Leander

Abstract

In this paper we consider the fundamental question of optimizing finite field multiplications with one fixed element. Surprisingly, this question did not receive much attention previously. We investigate which field representation, that is which choice of basis, allows for an optimal implementation. Here, the efficiency of the multiplication is measured in terms of the number of XOR operations needed to implement the multiplication. While our results are potentially of larger interest, we focus on a particular application in the second part of our paper. Here we construct new MDS matrices which outperform or are on par with all previous results when focusing on a round-based hardware implementation.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Published by the IACR in CRYPTO 2016
DOI
10.1007/978-3-662-53018-4_23
Keywords
finite fieldsmultiplicationXOR-countlightweight cryptographyMDS matricesblock cipher
Contact author(s)
christof beierle @ rub de
History
2017-02-17: last of 2 revisions
2016-02-14: received
See all versions
Short URL
https://ia.cr/2016/119
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2016/119,
      author = {Christof Beierle and Thorsten Kranz and Gregor Leander},
      title = {Lightweight Multiplication in GF(2^n) with Applications to MDS Matrices},
      howpublished = {Cryptology ePrint Archive, Paper 2016/119},
      year = {2016},
      doi = {10.1007/978-3-662-53018-4_23},
      note = {\url{https://eprint.iacr.org/2016/119}},
      url = {https://eprint.iacr.org/2016/119}
}
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