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Paper 2008/062
Computing Hilbert Class Polynomials
Juliana Belding and Reinier Broker and Andreas Enge and Kristin Lauter
Abstract
We present and analyze two algorithms for computing the Hilbert class polynomial H_D(X). The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing H_D(X), and we show that all methods have comparable run times.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- elliptic curve cryptographycomplex multiplication
- Contact author(s)
- klauter @ microsoft com
- History
- 2008-02-11: received
- Short URL
- https://ia.cr/2008/062
- License
-
CC BY