Common use of System setup phase Clause in Contracts

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.