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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 [[Menezes-Okamato-
to Logarithms in a Finite Field|journal=IEEE Transactions On Information Theory|date=1993|volume=39|issue=5}}</ref> pairings have also been used to construct many cryptographic systems for which no other efficient implementation is known, such as [[identity based encryption]] or [[attribute based encryption]] schemes.
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*[http://crypto.stanford.edu/pbc/ Ben Lynn's PBC Library]
▲[[Category:Elliptic curve cryptography]]
[[Category:Pairing-based cryptography| ]]
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