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Line 2: ==Definition== The following definition is commonly used in most academic papers.<ref>{{cite book\|last1=Koblitz\|first1=Neal\|last2=Menezes\|first2=Alfred\|title=Cryptography and Coding \|chapter=Pairing-Based cryptography at high security levels\|series=Lecture Notes in Computer Science\|date=2005\|volume=3796\|pages=13–36 \|doi=10.1007/11586821_2\|isbn=978-3-540-30276-6 }}</ref> 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:

Pairing-based cryptography: Difference between revisions