Revision as of 06:41, 11 August 2019 edit 178.197.227.16 (talk) →Definition: These are additive groups, so we need to use additive notation on their elements. The target group being multiplicative, the notation is correct on the right side. Tags: Mobile edit Mobile web edit ← Previous edit		Revision as of 00:33, 27 June 2020 edit undo BHGbot (talk \| contribs) 132,943 edits m WP:BHGbot 6 (List 5): eponymous category first, per MOS:CATORDER; WP:GENFIXES Tag: AWB Next edit →
Line 4: 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~~cyclic group~~\|cyclic groups~~]]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: ; [[Bilinearity]]: <math> \forall a,b \in F_q^,\ \forall P\in G_1, Q\in G_2:\ e\left(aP, bQ\right) = e\left(P, Q\right)^{ab}</math> ; [[Degeneracy (mathematics)\|Non-degeneracy]]: <math>e \neq 1</math> Line 40: [http://crypto.stanford.edu/pbc/ Ben Lynn's PBC Library] [[Category:Elliptic curve cryptography]]▼ [[Category:Pairing-based cryptography\| ]] ▲[[Category:Elliptic curve cryptography]]

Pairing-based cryptography: Difference between revisions