Paper 2004/189 Original: eprint.iacr.org/2004/189 ↗
Computing Modular Polynomials
Abstract
We present a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves and are useful in many aspects of computational number theory and cryptography. Our algorithm has the distinguishing feature that it does not involve the computation of Fourier coefficients of modular forms. We avoid computing the exponentially large integral coefficients by working directly modulo a prime and computing isogenies between elliptic curves via Velu's formulas.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2005-06-15: last updated
- 2004-08-07: published
- Short URL
- https://ia.cr/2004/189
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2004/189,
author = {Denis Charles and Kristin Lauter},
title = {Computing Modular Polynomials},
howpublished = {Cryptology {ePrint} Archive, Paper 2004/189},
year = {2004},
url = {https://eprint.iacr.org/2004/189}
}