Pairing-based cryptography: Difference between revisions

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'''Pairing-based cryptography''' is the use of a [[pairing]] between elements of two cryptographic [[Group (mathematics)|groups]] to a third group <math>e :G_1 \times G_2 \to G_T</math> to construct [[cryptography|cryptographic]] systems.

== Classification ==

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For example, in groups equipped with a [[bilinear mapping]] such as the [[Weil pairing]] or [[Tate pairing]], generalizations of the [[Diffie–Hellman problem|computational Diffie–Hellman problem]] are believed to be infeasible while the simpler [[decisional Diffie–Hellman assumption|decisional Diffie–Hellman problem]] can be easily solved using the pairing function. The first group is sometimes referred to as a '''Gap Group''' because of the assumed difference in difficulty between these two problems in the group.

While first used for [[cryptanalysis]]<ref>{{cite journal|last1=Menezes|first1=Alfred J. Menezes|last2=Okamato|first2=Tatsuaki|last3=Vanstone|first3=Scott A.|title=Reducing Elliptic Curve Logarithms

Pairingsto Logarithms in a Finite Field|journal=IEEE Transactions On Information Theory|date=1993|volume=39|issue=5}}</ref>, pairings have since been used to construct many cryptographic systems for which no other efficient implementation is known, such as [[identity based encryption]] or [[attribute based encryption]].

A contemporary example of using bilinear pairings is exemplified in the [[Boneh-Lynn-Shacham]] signature scheme.