Karabina, K.Knapp, E.Menezes, A.2016-02-082016-02-08201319305346http://hdl.handle.net/11693/21101For 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.EnglishAsymmetric pairingsCryptographyDiscrete logarithm problemVerheul's theoremArticle10.3934/amc.2013.7.103