Abstract
We propose several constructions for the original multiplication algorithm of D.V. and G.V. Chudnovsky in order to improve its scalar complexity. We highlight the set of generic strategies who underlay the optimization of the scalar complexity, according to parameterizable criteria. As an example, we apply this analysis to the construction of type elliptic Chudnovsky2 multiplication algorithms for small extensions. As a case study, we significantly improve the Baum-Shokrollahi construction for multiplication in \(\mathbb {F}_{256}/\mathbb {F}_{4}\).
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The authors wish to thank the anonymous referees for their valuable comments which greatly improved the quality of the manuscript.
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Ballet, S., Bonnecaze, A. & Dang, TH. Optimization of the scalar complexity of Chudnovsky2 multiplication algorithms in finite fields. Cryptogr. Commun. 13, 495–517 (2021). https://doi.org/10.1007/s12095-021-00494-y
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DOI: https://doi.org/10.1007/s12095-021-00494-y