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Dmjones500 (talk | contribs) m Link to description of cyclic groups |
→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 |
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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(
; [[Degeneracy (mathematics)|Non-degeneracy]]: <math>e \neq 1</math>
; Computability: There exists an efficient algorithm to compute <math>e</math>.
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