ABSTRACT
Definition 6.1 Let eˆ : G1 × G1 → G2 be a symmetric bilinear pairing defined in Section 2.2.4 and P be a generator of group G1. The generalized bilinear Diffie-Hellman problem (GBDHP) defined in < G1,G2, e > is described as follows: Given < P, aP, bP, cP > with uniformly random choices of a, b, c ∈ Z∗q, the goal of a GBDHP breaker is to output a pair < Q ∈ G∗1, e(P,Q)abc ∈ G2 >. We define the advantage of A as Adv(A), which is assumed to be negligible.
