Pairing-based cryptography: Difference between revisions

Revision as of 23:53, 10 January 2015

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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_T</math> be two cyclic groups of prime order <math>q</math>. A pairing is a map: <math> e: G_1 \times G_1G_2 \rightarrow G_T </math>, which satisfies the following properties:

# [[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>