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Pairing-based cryptography
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Pairing-based cryptography : ウィキペディア英語版
Pairing-based cryptography
Pairing-based cryptography is the use of a pairing between elements of two cryptographic groups to a third group with a mapping e :G_1 \times G_2 \to G_T to construct or analyze cryptographic systems.
==Definition==
The following definition is commonly used in most academic papers.
Let G_1, G_2 be two additive cyclic groups of prime order q, and G_T another cyclic group of order q written multiplicatively. A pairing is a map: e: G_1 \times G_2 \rightarrow G_T , which satisfies the following properties:
# Bilinearity: \forall a,b \in F_q^
*,\ \forall P\in G_1, Q\in G_2:\ e\left(a P, b Q\right) = e\left(P, Q\right)^
# Non-degeneracy: e\left(P, Q\right) \neq 1
# Computability: there exist an efficient algorithm to compute e.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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