Constructive membership in black-box groups
نویسنده
چکیده
We present an algorithm to reduce the constructive membership problem for a black-box group G to three instances of the same problem for involution centralisers in G. If G is a simple group of Lie type in odd characteristic, then this reduction can be performed in (Monte Carlo) polynomial time.
منابع مشابه
Quantum computation of discrete logarithms in semigroups
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor’s algorithms for period finding and discrete log 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 log problem are hard in semigroup...
متن کاملConstructive Membership Testing in Black-Box Classical Groups
1 School of Mathematics and Statistics, The University of Western Australia 35 Stirling Highway CRAWLEY WA 6009 Australia [email protected], [email protected] 2 Faculty of Information Sciences and Engineering, The University of Canberra, ACT, 2601 [email protected] 3 Centro de Álgebra da Universidade de Lisboa Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal csaba.schnei...
متن کاملFast constructive recognition of black box symplectic groups
We present an algorithm which, for any given black box group G isomorphic to Sp(d, q), constructs explicit inverse isomorphisms between G and the standard copy of Sp(d, q). We also report on the performance of an implementation of this algorithm in the group theory system GAP.
متن کاملFast constructive recognition of black box unitary groups∗
We present 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 oracles for handling SL(2, q) subgroups and for computing discrete logarithms in cyclic groups of order q ± 1.
متن کاملFast constructive recognition of black box orthogonal groups
We present an algorithm that constructively recognises when a given black box group is a nontrivial homomorphic image of the orthogonal group Ωε(d, q) for known ε, d and q. The algorithm runs in polynomial time assuming oracles for handling SL(2, q) subgroups and discrete logarithms in F∗q . © 2006 Elsevier Inc. All rights reserved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007