Common use of Setup Phase Clause in Contracts

Setup Phase. In this phase, the TTP selects the EC Ep(a,b) in Zp with generator point P of order q. It determines six hash functions H0 : {0, 1}∗ → Zq∗, H1 : Zq → Zq∗, H2 : {0, 1}∗ → Zq∗, H3 : Zq → Zq∗, H4 : {0, 1}∗ → Zq∗, and H5 : {0, 1}∗ → Zq∗. Also a symmetric key encryption algorithm is chosen to encrypt a message M into the ciphertext C using the secret shared key k, C = Ek(M), together with the corresponding decryption algorithm, M = Dk(C). A random value k is set as the private key of the TTP. The corresponding public key Ppub is computed by Ppub = kP. Now, the public parameters {Ep(a,b), Ppub, P, H0, H1, H2, H3, H4, H5, Ek(), Dk()} are published.