NATURAL REPRESENTATIONS OF BLACK BOX GROUPS ENCRYPTING SL2(Fq)

Creative Commons License

Yalçınkaya Ş., Borovik A.

Other, pp.1-15, 2020

  • Publication Type: Other Publication / Other
  • Publication Date: 2020
  • Page Numbers: pp.1-15
  • Istanbul University Affiliated: Yes

Abstract

Given a global exponent E for a black box group Y encrypting SL2(F), where F is an unknown finite field of unknown odd characteristic, we construct, in probabilistic time polynomial in log E, the isomorphisms

Y ←→ SL2(K),

where K is a black box field encrypting F. Our algorithm makes no reference to any additional oracles. We also give similar algorithms for black box groups encrypting PGL2(F), PSL2(F).