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Fast Constructive Recognition of Black-Box Unitary Groups

Published online by Cambridge University Press:  01 February 2010

Peter A. Brooksbank
Peter A. Brooksbank
Affiliation:
Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus OH 43210, USAbrooksbank@math.ohio-state.edu, http://www.math.ohio-state.edu/~brooksbank

Abstract

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In this paper, the author presents a new algorithm to recognise, constructively, when a given black-box group is a homomorphic image of the unitary group SU(d, q) for known d and q. The algorithm runs in polynomial time, assuming the existence of oracles for handling SL(2, q) subgroups, and for computing discrete logarithms in cyclic groups of order q ± 1.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 6 , 2003 , pp. 162 - 197
Copyright
Copyright © London Mathematical Society 2003

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