An Efficient ASBB Scheme Sample Clauses

An Efficient ASBB Scheme. ‌ The scheme is realized in bilinear pairing groups [5, 16]. Let PairGen be an algo- rithm that, on input a security parameter 1λ, outputs a tuple Υ = (p, G, GT , e), where G and GT have the same prime order p, and e : G× G → GT is an efficient non-degenerate bilinear map such that e(g, g) ƒ= 1 for any generator g of G, and for all u, v ∈ Z, it holds that e(gu, gv) = e(g, g)uv . { } → ← ( ) – Public parameters: Let Υ = (p, G, GT , e) PairGen(1λ), G = g . Let H : 0, 1 ∗ G be a cryptographic hash function. The system parameters are π = (Υ, g, H). – Public/secret keys: Select at random r ∈ Zp∗, X ∈ G \ {1}. Compute R = g−r, A = e(X, g). The public key is pk = (R, A) and the secret key is sk = (r, X). – Sign: The signature of any string s ∈ {0, 1}∗ under the public key pk is σ = XH(s)r. – Verify: Given a message-signature pair (s, σ), the verification equation is e(σ, g)e(H(s), R) = A. If the equation holds, output 1 to represent that purported signature is valid. Else output 0 and reject the purported signature.