Structure computation and discrete logarithms in finite abelian p-groups

Details Structure computation and discrete logarithms in finite abelian p-groups Structure computation and discrete logarithms in finite abelian p-groups

2008-09-19

arxiv.org/abs/0809.3413v3

Math. Comp. 80 (2011), 477-500

Mathematics

Number Theory

23 pages, minor edits

Scientific paper

We present a generic algorithm for computing discrete logarithms in a finite abelian p-group H, improving the Pohlig-Hellman algorithm and its generalization to noncyclic groups by Teske. We then give a direct method to compute a basis for H without using a relation matrix. The problem of computing a basis for some or all of the Sylow p-subgroups of an arbitrary finite abelian group G is addressed, yielding a Monte Carlo algorithm to compute the structure of G using O(|G|^0.5) group operations. These results also improve generic algorithms for extracting pth roots in G.

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