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

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 all previous results when focusing on a round-based hardware implementation.

• Type: Journal
• Year: 2016
• Where: IACR
• Authors: Christof Beierle, Thorsten Kranz, Gregor Leander
• Keywords: Biometrics, IACR 2016