An L(1/3) algorithm for discrete logarithm computation and principality testing in certain number fields

Details An L(1/3) algorithm for discrete logarithm computation and principality testing in certain number fields An L(1/3) algorithm for discrete logarithm computation and principality testing in certain number fields

2012-04-05

arxiv.org/abs/1204.1292v1

Mathematics

Number Theory

13 pages

Scientific paper

We analyse the complexity of solving the discrete logarithm problem and of testing the principality of ideals in a certain class of number fields. We achieve the 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, Gaudry and Thom\'{e} in the context of algebraic curves over finite fields.

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