Abstract
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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Belding, J., Bröker, R., Enge, A., Lauter, K. (2008). Computing Hilbert Class Polynomials. In: van der Poorten, A.J., Stein, A. (eds) Algorithmic Number Theory. ANTS 2008. Lecture Notes in Computer Science, vol 5011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79456-1_19
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DOI: https://doi.org/10.1007/978-3-540-79456-1_19
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