Computation of Hilbert class polynomials and modular polynomials from supersingular elliptic curves
Number Theory
2023-12-18 v2
Abstract
We present several new heuristic algorithms to compute class polynomials and modular polynomials modulo a prime by revisiting the idea of working with supersingular elliptic curves. The best known algorithms to this date are based on ordinary curves, due to the supposed inefficiency of the supersingular case. While this was true a decade ago, the recent advances in the study of supersingular curves through the Deuring correspondence motivated by isogeny-based cryptography has provided all the tools to perform the necessary tasks efficiently.
Cite
@article{arxiv.2301.08531,
title = {Computation of Hilbert class polynomials and modular polynomials from supersingular elliptic curves},
author = {Antonin Leroux},
journal= {arXiv preprint arXiv:2301.08531},
year = {2023}
}