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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 with a mapping <math>e :G_1 \times G_2 \to G_T</math> to construct or analyze [[cryptography|cryptographic]] systems.
==Definition==
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# [[Bilinearity]]: <math> \forall a,b \in F_q^*,\ \forall P,Q \in G_1:\ e\left(P^a, Q^b\right) = e\left(P, Q\right)^{ab}</math>
# [[Degeneracy (mathematics)|Non-degeneracy]]: <math>e\left(P, Q\right) \neq 1</math>
# Computability: there exist an efficient algorithm to compute <math>e</math>.
== Classification ==
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