GENERALIZATIONS OF VERHEUL'S THEOREM TO ASYMMETRIC PAIRINGS

被引：0

作者：

Karabina, Koray ^{[1
]}

Knapp, Edward ^{[2
]}

Menezes, Alfred ^{[3
]}

机构：

[1] Bilkent Univ, Dept Math, TR-06800 Ankara, Turkey

[2] Google Inc, Mountain View, CA 94043 USA

[3] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2013年 / 7卷 / 01期

关键词：

Verheul's theorem; asymmetric pairings; cryptography; discrete logarithm problem; LOGARITHMS; INVERSION; FORMULAS; CURVES;

D O I：

10.3934/amc.2013.7.103

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

For symmetric pairings e:GxG -> G(T), Verheul proved that the existence of an efficiently-computable isomorphism phi:G(T)-> G implies that the Diffie-Hellman problems in G and G(T) can be efficiently solved. In this paper, we explore the implications of the existence of efficiently-computable isomorphisms phi(1):G(T)-> G(1) and phi(2):G(T)-> G(2) for asymmetric pairings e:G(1)xG(2)-> G(T). We also give a simplified proof of Verheul's theorem.

引用

页码：103 / 111

页数：9

共 24 条

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[Anonymous], 2005, PAIRINGS

[2]

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[3]

Barreto PSLM, 2006, LECT NOTES COMPUT SC, V3897, P319

[4] Short signatures from the Weil pairing [J].