Chávez-Saab, J.; Ortega, O.; Pizarro-Madariaga, A. On the Parallelization of Square-Root Vélu’s Formulas. Math. Comput. Appl.2024, 29, 14.
Chávez-Saab, J.; Ortega, O.; Pizarro-Madariaga, A. On the Parallelization of Square-Root Vélu’s Formulas. Math. Comput. Appl. 2024, 29, 14.
Chávez-Saab, J.; Ortega, O.; Pizarro-Madariaga, A. On the Parallelization of Square-Root Vélu’s Formulas. Math. Comput. Appl.2024, 29, 14.
Chávez-Saab, J.; Ortega, O.; Pizarro-Madariaga, A. On the Parallelization of Square-Root Vélu’s Formulas. Math. Comput. Appl. 2024, 29, 14.
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, we introduce a theoretical framework for parallelizing isogeny computations and provide a proof-of-concept implementation in C with OpenMP. While the parallelization effectiveness exhibits diminishing returns with the number of cores, we still obtain strong results when using a small number of cores. Concretely, our implementation shows that for large degrees it is easy to achieve speedup factors of up to 1.74, 2.54 and 3.44 for 2, 4 and 8 cores, respectively.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
