System setup phase Sample Clauses

System setup phase. The server chooses an elliptic curve equation Ep (a, b) with the order n , which is defined in Section 3.

System setup phase. Given a security parameter k, the server S generates the system parameters as follows. (1) Choose a finite field Fp, where p is a k-bit prime. (2) Define an elliptic curve E : y2 ≡ x3 + ax + b mod p over Fp, where a, b ∈ Fp, p ≥ 3, 4a3 + 27b2 /= 0 mod p. (3) Choose a public point P with prime order q over E, and generate a cyclic additive group G of order q by point (4) Choose a random number s ∈ Z∗ as the master key and set Ppub = sP as the system public key. (5) Choose four cryptographic hash functions H1 : {0, 1}∗ × G → Z∗, H2 : {0, 1}∗ × G3 → {0, 1}k, H3 : {0, 1}∗ × G4 → {0, 1}k and H4 : {0, 1}∗ × G5 → {0, 1}k. (6) Publish the system parameters params = (Fq, E, G, P, Ppub, H1, H2, H3, H4) while keeping s secret.

System setup phase. System setup is performed by GWN as follows, 1. GWN chooses a non-singular elliptic curve Ep(a, b) over a prime finite Zp, where p is a large prime. Let G be an elliptic curve group. Then, GWN chooses a generator P of order q over Ep. GWN selects its private key dGWN and computes the public key QGWN = dGWN P in accordance with dGWN. } 2. GWN selects three collision-resistant one-way hash functions h, H1, H2 : {0, 1}∗ → Zq. 3. Finally, the system parameters params = Ep(a, b), P, p, q, h, H1, H2, QGWN is published while the private key dGWN is kept secretly by GWN.

System setup phase. Initially, the SA determines a large prime p and a