Pairing-based cryptography: Difference between revisions

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'''Pairing-based cryptography''' is the use of a [[pairing|pairing]] between elements of two [[Group (mathematics)|groups]] to a third group to construct [[cryptography|cryptographic]] systems. Usually the same group is used for the first two groups, making the pairing in fact a [[Map_(mathematics)|mapping]] from two elements from one group to an element form a second group. In this way, pairings can be used to reduce a hard problem in one group to a different, usually easier problem in another group.

'''Pairing-based cryptography''' is the idea is the construction of a mapping between two useful cryptographic groups

which allows for new cryptographic schemes based on the reduction of one problem in one

group to a different, usually easier problem in the other group.[http://theory.lcs.mit.edu/classes/6.897/spring04/L25.pdf].

For example, in groups equipped with a [[bilinear mapping]] such as the [[Weil pairing]] or [[Tate pairing]], generalizations of the [[Diffie-Hellman problem]] are believed to be computationally infeasible while the simpler [[Decisional Diffie-Hellman assumption|Decision 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.

The first group that is being mapped is called the Gap Group.

While first used for [[cryptanalysis]], pairings have since been used to construct many cryptographic systems for which no other efficient implementation is known, such as [[identity based encryption]] .

==External links==

*[http://theory.lcs.mit.edu/classes/6.897/spring04/L25.pdf Lecture on Pairing-Based Cryptography]

*[http://planeta.terra.com.br/informatica/paulobarreto/pblounge.html The Pairing-Based Crypto Lounge]

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