A low-memory algorithm for finding short product representations in finite groups
Identifieur interne : 002779 ( Main/Exploration ); précédent : 002778; suivant : 002780A low-memory algorithm for finding short product representations in finite groups
Auteurs : Gaetan Bisson [France, Pays-Bas] ; Andrew V. Sutherland [États-Unis]Source :
- Designs, Codes and Cryptography [ 0925-1022 ] ; 2012-04-01.
English descriptors
Abstract
Abstract: We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-ρ approach. Given an element z and a sequence of elements S, our algorithm attempts to find a subsequence of S whose product in G is equal to z. For a random sequence S of length d log2 n, where n = #G and d ≥ 2 is a constant, we find that its expected running time is $${O(\sqrt{n}\,{\rm log}\,n)}$$ group operations (we give a rigorous proof for d > 4), and it only needs to store O(1) group elements. We consider applications to class groups of imaginary quadratic fields, and to finding isogenies between elliptic curves over a finite field.
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DOI: 10.1007/s10623-011-9527-8
Affiliations:
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