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

Date: received 20 Jul 2019

Contact author: qtan016pg at e ntu edu sg,thomas peyrin@ntu edu sg

Available format(s): PDF | BibTeX Citation

Version: 20190722:072303 (All versions of this report)

Short URL: ia.cr/2019/847


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