Generalizations of verheul's theorem to asymmetric pairings

Date
2013
Authors
Karabina, K.
Knapp, E.
Menezes, A.
Advisor
Instructor
Source Title
Advances in Mathematics of Communications
Print ISSN
19305346
Electronic ISSN
Publisher
Volume
7
Issue
1
Pages
103 - 111
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
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.

Course
Other identifiers
Book Title
Keywords
Asymmetric pairings, Cryptography, Discrete logarithm problem, Verheul's theorem
Citation
Published Version (Please cite this version)