Natural representations of black box groups encrypting SL₂(\mathbbF_q)

2020/01/28 by Borovik, Alexandre, Yalçınkaya, Şükrü · 1 citation
#20P05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2001.10292

Abstract

Given a global exponent E for a black box group Y encrypting \rm SL₂(\mathbbF), where \mathbbF is an unknown finite field of unknown odd characteristic, we construct, in probabilistic time polynomial in log E, the isomorphisms Y \longleftrightarrow \rm SL₂(K), where K is a black box field encrypting \mathbbF. Our algorithm makes no reference to any additional oracles. We also give similar algorithms for black box groups encrypting \rm PGL₂(\mathbbF), \rm PSL₂(\mathbbF).

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• An implementation of the morphisms SL₂(\mathbbF) → SL₂(K) → X

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