Black box, white arrow

Borovik, Alexandre and Yalcinkaya, Sukru (2014) Black box, white arrow. [MIMS Preprint]

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The present paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. Instead of a single black box, we consider categories of black boxes and their morphisms. This makes new classes of black box problems accessible. For example, we can enrich black box groups by actions of outer automorphisms. As an example of application of this technique, we construct Frobenius maps on black box groups of untwisted Lie type in odd characteristic (Section 6) and inverse-transpose automorphisms on black box groups encrypting (P)SL_n(F_q). One of the advantages of our approach is that it allows us to work in black box groups over finite fields of big characteristic. Another advantage is the explanatory power of our methods; as an example, we explain Kantor's and Kassabov's construction of an involution in black box groups encrypting SL_2(2^n). Due to the nature of our work we also have to discuss a few methodological issues of the black box group theory.

Item Type: MIMS Preprint
Uncontrolled Keywords: black box group, morphism, polynomial time
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Prof Alexandre Borovik
Date Deposited: 02 May 2014
Last Modified: 08 Nov 2017 18:18

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