2024
DOI: 10.20944/preprints202401.1366.v1
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On the Parallelization of Square-Root Vélu’s Formulas

Jorge Chávez-Saab,
Odalis Ortega,
Amalia Pizarro-Madariaga

Abstract: A primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies. This computation traditionally relied on Vélu’s formulas, an approach with time complexity linear in the degree but which was further enhanced by Bernstein, De Feo, Leroux, and Smith to a square-root complexity. The improved square-root Vélu’s formulas exhibit a degree of parallelizability which has not been exploited in major implementations. In this study… Show more

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