Bilinear Maps Sample Clauses

Bilinear Maps properties: 9.3.1 A bilinear map is a function e : G × G → H (G is a group of order q and H is a group) with the 1. Bilinear: ∀x, y ∈ Zq e (g , g ) = e (g, g ) = e (g, g) 2. Non-degenerate: e (g, g) /= 1H We are interested in groups that have bilinear maps, but we still want groups that Discrete Log is still hard on them. So what properties can we expect from G? • DL is hard (Note that if DL is easy on H then you can also solve DL on G by simply looking at e (g, g e (g, g)x). We can, and want to have that property.

Bilinear Maps. We review the basic notations of the bilinear maps [3, 25] under our proposal. Let (G1, +) and (GT , ∗) be two groups of prime order q > 2k for a security parameter k ∈ N . A function e : G1×G1 −→ GT is said to be a bilinear map if it satisfies the following properties:

Bilinear Maps. × → • ∈ ∈

Bilinear Maps. Let G1 be a cyclic additive group with prime order q and G2 be a cyclic multiplicative group with the same prime order q. The bilinear map is denoted as the mapping e : G1 × G1 → G2, which has the following properties: (1) Bilinearity (2) Nondegeneracy (3) Efficiency