2003 | OriginalPaper | Chapter
On Class Group Computations Using the Number Field Sieve
Authors : Mark L. Bauer, Safuat Hamdy
Published in: Advances in Cryptology - ASIACRYPT 2003
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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The best practical algorithm for class group computations in imaginary quadratic number fields (such as group structure, class number, discrete logarithm computations) is a variant of the quadratic sieve factoring algorithm. Paradoxical as it sounds, the principles of the number field sieve, in a strict sense, could not be applied to number field computations, yet. In this article we give an indication of the obstructions.In particular, we first present fundamental core elements of a number field sieve for number field computations of which it is absolutely unknown how to design them in a useful way. Finally, we show that the existence of a number field sieve for number field computations with a running time asymptotics similar to that of the genuine number field sieve likely implies the existence of an algorithm for elliptic curve related computational problems with subexponential running time.