Open AccessShorter Linear Straight-Line Programs for MDS Matrices
Author(s) -
Thorsten Kranz,
Gregor Leander,
Ko Stoffelen,
Friedrich Wiemer
Publication year - 2017
Publication title -
iacr transaction on symmetric cryptology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.715
H-Index - 10
ISSN - 2519-173X
DOI - 10.46586/tosc.v2017.i4.188-211
Subject(s) - implementation , heuristics , matrix multiplication , work (physics) , line (geometry) , matrix (chemical analysis) , computer science , multiplication (music) , parallel computing , mathematical optimization , algorithm , mathematics , combinatorics , programming language , engineering , mechanical engineering , physics , geometry , materials science , quantum mechanics , composite material , quantum
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.