Paper 2009/445 Original: eprint.iacr.org/2009/445 ↗
Computing Hilbert class polynomials with the Chinese Remainder Theorem
Abstract
We present a space-efficient algorithm to compute the Hilbert class polynomial H_D(X) modulo a positive integer P, based on an explicit form of the Chinese Remainder Theorem. Under the Generalized Riemann Hypothesis, the algorithm uses O(|D|^(1/2+o(1))log P) space and has an expected running time of O(|D|^(1+o(1)). We describe practical optimizations that allow us to handle larger discriminants than other methods, with |D| as large as 10^13 and h(D) up to 10^6. We apply these results to construct pairing-friendly elliptic curves of prime order, using the CM method.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2009-09-14: last updated
- 2009-09-14: published
- Short URL
- https://ia.cr/2009/445
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2009/445,
author = {Andrew V. Sutherland},
title = {Computing Hilbert class polynomials with the Chinese Remainder Theorem},
howpublished = {Cryptology {ePrint} Archive, Paper 2009/445},
year = {2009},
url = {https://eprint.iacr.org/2009/445}
}