Quantum period reconstruction of approximate sequences

Authors:
Igor E. Shparlinski;Arne Winterhof
Affiliations:
Department of Computing, Macquarie University, North Ryde, NSW 2109, Australia;Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Straße 69, A-4040 Linz, Austria
Venue:
Information Processing Letters
Year:
2007

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Abstract

We consider the problem of determining the period of a sequence over an unknown finite field, given a black-box which returns only a few most significant bits of the sequence elements. For sequences with small autocorrelation we prove the existence of a polynomial time quantum algorithm for the above problem based on an algorithm of Hales and Hallgren.