CryptoDB
Improved Heuristics for Short Linear Programs
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| Abstract: | In this article, we propose new heuristics for minimising the amount of XOR gates required to compute a system of linear equations in GF(2). We first revisit the well known Boyar-Peralta strategy and argue that a proper randomisation process during the selection phases can lead to great improvements. We then propose new selection criteria and explain their rationale. Our new methods outperform state-of-the-art algorithms such as Paar or Boyar-Peralta (or open synthesis tools such as Yosys) when tested on random matrices with various densities. They can be applied to matrices of reasonable sizes (up to about 32 × 32). Notably, we provide a new implementation record for the matrix underlying the MixColumns function of the AES block cipher, requiring only 94 XORs. |
Video from TCHES 2019
BibTeX
@article{tches-2019-29960,
title={Improved Heuristics for Short Linear Programs},
journal={IACR Transactions on Cryptographic Hardware and Embedded Systems},
publisher={Ruhr-Universität Bochum},
volume={2020, Issue 1},
pages={203-230},
url={https://tches.iacr.org/index.php/TCHES/article/view/8398},
doi={10.13154/tches.v2020.i1.203-230},
author={Quan Quan Tan and Thomas Peyrin},
year=2019
}