Cryptology ePrint Archive: Report 2019/847

Improved Heuristics for Short Linear Programs

Quan Quan Tan and Thomas Peyrin

Abstract: In this article, we propose new heuristics for minimizing 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 randomization 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 on matrices of reasonable sizes (up to about 32 x 32). Notably, we provide a new implementation record for the matrix underlying the MixColumns function of the AES block cipher, requiring only 94 XORs.

Category / Keywords: implementation / XOR gate, gate count, linear system, diffusion matrices

Original Publication (in the same form): IACR-CHES-2020
DOI:
10.13154/tches.v2020.i1.203-230

Date: received 20 Jul 2019, last revised 28 Jan 2020

Contact author: quanquan001 at e ntu edu sg, thomas peyrin at ntu edu sg

Available format(s): PDF | BibTeX Citation

Version: 20200128:070806 (All versions of this report)

Short URL: ia.cr/2019/847


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