[Resource Topic] 2016/119: Lightweight Multiplication in GF(2^n) with Applications to MDS Matrices

Welcome to the resource topic for 2016/119

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

Authors: Christof Beierle, Thorsten Kranz, Gregor Leander


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.

ePrint: https://eprint.iacr.org/2016/119

Talk: https://www.youtube.com/watch?v=BF1rT3M9Ukk

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