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Conference Papers Year : 2008

Computing Hilbert Class Polynomials

Juliana Belding
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Reinier Bröker
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Andreas Enge
Kristin Lauter
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We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . 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 $H_D$ , and we show that all methods have comparable run times.
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inria-00246115 , version 1 (07-02-2008)


  • HAL Id : inria-00246115 , version 1
  • ARXIV : 0802.0979


Juliana Belding, Reinier Bröker, Andreas Enge, Kristin Lauter. Computing Hilbert Class Polynomials. ANTS-VIII - Eighth Algorithmic Number Theory Symposium, May 2008, Banff, Canada. pp.282-295. ⟨inria-00246115⟩
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