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      Generalizations of verheul's theorem to asymmetric pairings

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      Author(s)
      Karabina, K.
      Knapp, E.
      Menezes, A.
      Date
      2013
      Source Title
      Advances in Mathematics of Communications
      Print ISSN
      19305346
      Volume
      7
      Issue
      1
      Pages
      103 - 111
      Language
      English
      Type
      Article
      Item Usage Stats
      138
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      Abstract
      For symmetric pairings e: G × G → GT, Verheul proved that the existence of an efficiently-computable isomorphism Φ: GT → G implies that the Diffie-Hellman problems in G and GT can be efficiently solved. In this paper, we explore the implications of the existence of efficiently-computable isomorphisms Φ1: GT →G1 and Φ2: GT →G2 for asymmetric pairings e: G1 × G2 → GT. We also give a simplified proof of Verheul's theorem. © 2013 AIMS.
      Keywords
      Asymmetric pairings
      Cryptography
      Discrete logarithm problem
      Verheul's theorem
      Permalink
      http://hdl.handle.net/11693/21101
      Published Version (Please cite this version)
      http://dx.doi.org/10.3934/amc.2013.7.103
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      • Department of Mathematics 653
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