Shorter Linear Straight-Line Programs for MDS Matrices

  • Thorsten Kranz Horst Görtz Institute for IT Security, Ruhr-Universität Bochum
  • Gregor Leander Horst Görtz Institute for IT Security, Ruhr-Universität Bochum
  • Ko Stoffelen Digital Security Group, Radboud University, Nijmegen
  • Friedrich Wiemer Horst Görtz Institute for IT Security, Ruhr-Universität Bochum
Keywords: XOR Count, MDS, Linear Layer, Shortest Straight-Line Program, SAT

Abstract

Recently a lot of attention is paid to the search for efficiently implementable MDS matrices for lightweight symmetric primitives. Most previous work concentrated on locally optimizing the multiplication with single matrix elements. Separate from this line of work, several heuristics were developed to find shortest linear straightline programs. Solving this problem actually corresponds to globally optimizing multiplications by matrices. In this work we combine those, so far largely independent lines of work. As a result, we achieve implementations of known, locally optimized, and new MDS matrices that significantly outperform all implementations from the literature. Interestingly, almost all previous locally optimized constructions behave very similar with respect to the globally optimized implementation. As a side effect, our work reveals the so far best implementation of the Aes Mix- Columns operation with respect to the number of XOR operations needed.
Published
2017-12-15
How to Cite
Kranz, T., Leander, G., Stoffelen, K., & Wiemer, F. (2017). Shorter Linear Straight-Line Programs for MDS Matrices. IACR Transactions on Symmetric Cryptology, 2017(4), 188-211. https://doi.org/10.13154/tosc.v2017.i4.188-211
Section
Articles