Cryptology ePrint Archive: Report 2016/119

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

Christof Beierle and 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.

Category / Keywords: secret-key cryptography / finite fields, multiplication, XOR-count, lightweight cryptography, MDS matrices, block cipher

Original Publication (in the same form): IACR-CRYPTO-2016

Date: received 11 Feb 2016, last revised 17 Feb 2017

Contact author: christof beierle at rub de

Available format(s): PDF | BibTeX Citation

Version: 20170217:150415 (All versions of this report)

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