STRUCTURE COMPUTATION AND DISCRETE LOGARITHMS IN FINITE ABELIAN p-GROUPS
Andrew V. Sutherland · 2011
Abstract. 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 | 1/2) group operations. These results also improve generic algorithms for extracting pth roots in G. 1.