2023/01/20 by Antonin Leroux, Leroux, Antonin · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2301.08531
openalex publication_date 2023/01/20 · openalex created_date 2023/01/24 · openalex updated_date 2026/07/28
We present several new heuristic algorithms to compute class polynomials and modular polynomials modulo a prime p 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.