Strongly Fair Validity Clause Samples

Strongly Fair Validity. We first show that the probability is exactly lower-bounded by the uniform distribution in the ideal world. Then, we show that RBA works the same as the ideal world except the negligible probability. We define the VRF oracle, consisting of two algorithm: Oprove and Overi. Oprove is defined as: 1) Take as input a seed x and a secret key sk. 2) Return Prove(x, sk). Overi is defined as: 1) Take as input a public key pk, a seed x, a value y and a proof π. 2) Return Veri(pk, x, y, π). We also define the ideal functionality of VRF, consisting of two algorithm: Iprove and Iveri. Iprove is defined as: 1) Takes as input a seed x and a secret key sk. Y . Σ k−1 t − i n − i ( n − t ) n . t Σk ( n − t ). n 2) Check whether Q(x, sk) is defined. If not, choose y ← Thus, in expectation, the number of rounds can be computed Q(x, sk) = (y, π). If Q(x, sk) is defined, prove(x, sk) ≤ return Q(x, sk). Σ . Σ by ▇▇▇▇▇ is defined as: − · t n t 4 t ( ) · (6 + 4i) ≤ 6 + n . 1) Takes as input a public key pk, a seed x, a value y and ≥ ≥