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someone changed the definition incorrectly years ago |
Dmjones500 (talk | contribs) m Link to description of cyclic groups |
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The following definition is commonly used in most academic papers.<ref>{{cite journal|last1=Koblitz|first1=Neal|last2=Menezes|first2=Alfred|title=Pairing-Based cryptography at high security levels|journal=LNCS|date=2005|volume=3796}}</ref>
Let <math>G_1, G_2</math> be two additive [[Cyclic group|cyclic groups]] 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:
; [[Bilinearity]]: <math> \forall a,b \in F_q^*,\ \forall P\in G_1, Q\in G_2:\ e\left(P^a, Q^b\right) = e\left(P, Q\right)^{ab}</math>
; [[Degeneracy (mathematics)|Non-degeneracy]]: <math>e \neq 1</math>
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