Author:
Childs Andrew M.,Ivanyos Gábor
Abstract
AbstractWe describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and the discrete logarithm problem as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks. In contrast, we show that some generalizations of the discrete logarithm problem are hard in semigroups despite being easy in groups. We relate a shifted version of the discrete logarithm problem in semigroups to the dihedral hidden subgroup problem, and we show that the constructive membership problem with respect to
Funder
NSERC
Ontario Ministry of Research and Innovation
US ARO
Hungarian Research Fund
Centre for Quantum Technologies at the National University of Singapore
Subject
Applied Mathematics,Computational Mathematics,Computer Science Applications
Cited by
22 articles.
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