Cryptology ePrint Archive: Report 2020/903

Optimizing Implementations of Linear Layers

Zejun Xiang and Xiangyong Zeng and Da Lin and Zhenzhen Bao and Shasha Zhang

Abstract: In this paper, we propose a new heuristic algorithm to search efficient implementations (in terms of Xor count) of linear layers used in symmetric-key cryptography. It is observed that the implementation cost of an invertible matrix is related to its matrix decomposition if sequential-Xor (s-Xor) metric is considered, thus reducing the implementation cost is equivalent to constructing an optimized matrix decomposition. The basic idea of this work is to find various matrix de- compositions for a given matrix and optimize those decompositions to pick the best implementation. In order to optimize matrix decompositions, we present several ma- trix multiplication rules over F2, which are proved to be very powerful in reducing the implementation cost. We illustrate this heuristic by searching implementations of several matrices proposed recently and matrices already used in block ciphers and Hash functions, and the results show that our heuristic performs equally good or outperforms Paar’s and Boyar-Peralta’s heuristics in most cases.

Category / Keywords: implementation / Linear Layer and Implementation and Xor Count and AES

Original Publication (with minor differences): IACR-FSE-2020

Date: received 17 Jul 2020

Contact author: xiangzejun at hubu edu cn

Available format(s): PDF | BibTeX Citation

Version: 20200718:161312 (All versions of this report)

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