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==Definition==
The following definition is commonly used in most academic papers.<ref>{{cite
Let <math>F_q</math> be a [[Finite field]] over prime <math>q</math>, <math>G_1, G_2</math> two additive [[cyclic group]]s of prime order <math>q</math> and <math>G_T</math> another cyclic group of order <math>q</math> written multiplicatively. A pairing is a map: <math> e: G_1 \times G_2 \rightarrow G_T </math>, which satisfies the following properties:
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