chapter  3
32 Pages

Pairings Sorina Ionica and Damien Robert

We recall from Section 1.2 that a pairing is a map e : G1 × G2 → GT between finite abelian groups G1, G2 and GT , that satisfies the following conditions:

• e is bilinear, which means that e(P + Q,R) = e(P,R) × e(Q,R) and e(P,Q + R) = e(P,Q)× e(P,R);

• e is non-degenerate, which means that for any P ∈ G1 there is a Q ∈ G2 such that e(P,Q) 6= 1, and for any Q ∈ G2 there is a P ∈ G1 such that e(P,Q) 6= 1.