Structure computation and discrete logarithms in finite abelian $p$-groups
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- by Andrew V. Sutherland PDF
- Math. Comp. 80 (2011), 477-500
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 $p$th roots in $G$.References
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Additional Information
- Andrew V. Sutherland
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 852273
- ORCID: 0000-0001-7739-2792
- Email: drew@math.mit.edu
- Received by editor(s): September 19, 2008
- Received by editor(s) in revised form: July 27, 2009, and August 29, 2009
- Published electronically: April 16, 2010
- © Copyright 2010 by the author
- Journal: Math. Comp. 80 (2011), 477-500
- MSC (2010): Primary 11Y16; Secondary 20K01, 12Y05
- DOI: https://doi.org/10.1090/S0025-5718-10-02356-2
- MathSciNet review: 2728991