An L(1/3) algorithm for ideal class group and regulator computation in certain number fields

Details An L(1/3) algorithm for ideal class group and regulator computation in certain number fields An L(1/3) algorithm for ideal class group and regulator computation in certain number fields

2009-12-10

arxiv.org/abs/0912.1927v1

Computer Science

Cryptography and Security

Scientific paper

We analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs from Buchmann's, who proved a complexity bound of L(1/2,O(1)) when the discriminant tends to infinity with fixed degree. We achieve a subexponential complexity in O(L(1/3,O(1))) when both the discriminant and the degree of the extension tend to infinity by using techniques due to Enge and Gaudry in the context of algebraic curves over finite fields.

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