Abstract
The linear layer, which is basically a binary non-singular matrix, is an integral part of cipher construction in a lot of private key ciphers. As a result, optimising the linear layer for device implementation has been an important research direction for about two decades. The Boyar-Peralta’s algorithm (SEA’10) is one such common algorithm, which offers significant improvement compared to the straightforward implementation. This algorithm only returns implementation with XOR2 gates, and is deterministic. Over the last couple of years, some improvements over this algorithm has been proposed, so as to make support for XOR3 gates as well as make it randomised. In this work, we take an already existing improvement (Tan and Peyrin, TCHES’20) that allows randomised execution and extend it to support three input XOR gates. This complements the other work done in this direction (Banik et al., IWSEC’19) that also supports XOR3 gates with randomised execution. Further, noting from another work (Maximov, Eprint’19), we include one additional tie-breaker condition in the original Boyar-Peralta’s algorithm. Our work thus collates and extends the state-of-the-art, at the same time offers a simpler interface. We show several results that improve from the lastly best-known results.
This paper combines and extends from [5, 6, 10]. An extended version of this paper is available at [3]. The first author would like to thank Sylvain Guilley (Télécom-Paris; Secure-IC) for providing the gate costs in the STM 130 nm (ASIC4) library.
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Notes
- 1.
Available at https://bitbucket.org/vdasu_edu/boyar-peralta-xor3/.
- 2.
The algorithm in [10], with the kind permission from the authors, is available within our implementation (the relevant source-code is written by us).
- 3.
- 4.
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Baksi, A., Dasu, V.A., Karmakar, B., Chattopadhyay, A., Isobe, T. (2021). Three Input Exclusive-OR Gate Support for Boyar-Peralta’s Algorithm. In: Adhikari, A., Küsters, R., Preneel, B. (eds) Progress in Cryptology – INDOCRYPT 2021. INDOCRYPT 2021. Lecture Notes in Computer Science(), vol 13143. Springer, Cham. https://doi.org/10.1007/978-3-030-92518-5_7
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