Abstract
Although the supersingular isogeny Diffie-Hellman (SIDH) protocol is one of the most promising post-quantum cryptosystems, it is significantly slower than its main counterparts due to the underlying large smooth-degree isogeny computation. In this work, we address the problem of evaluating and constructing a strategy for computing the large smooth-degree isogeny in the multi-processor setting by formulating them as scheduling problems with dependencies. The contribution of this work is two-fold. For the strategy evaluation, we transform strategies into task dependency graphs and apply precedence-constrained scheduling algorithms to them in order to find their costs. For the strategy construction, we construct strategies from smaller parts that are optimal solutions of integer programming representing the problem. We show via experiments that the proposed two techniques together offer more than 13% reduction in the strategy costs compared to the best current results by Hutchinson and Karabina presented at Indocrypt 2018.
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Acknowledgement
The authors would like to thank Jason LeGrow and the reviewers for their constructive comments on improving the manuscript. The first author would like to thank Francisco Rodríguez-Henríquez and Kittiphop Phalakarn for their valuable feedback. The first author is supported by the Ripple Impact Fund through a Ripple Graduate Fellowship. The second author is supported by JSPS Grant-in-Aid for Transformative Research Areas A grant number JP21H05845.
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Phalakarn, K., Suppakitpaisarn, V., Hasan, M.A. (2022). Speeding-Up Parallel Computation of Large Smooth-Degree Isogeny Using Precedence-Constrained Scheduling. In: Nguyen, K., Yang, G., Guo, F., Susilo, W. (eds) Information Security and Privacy. ACISP 2022. Lecture Notes in Computer Science, vol 13494. Springer, Cham. https://doi.org/10.1007/978-3-031-22301-3_16
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