A Threshold Pseudorandom Function Construction and Its Applications

We give the first construction of a practical threshold pseudorandom function. The protocol for evaluating the function is efficient enough that it can be used to replace random oracles in some protocols relying on such oracles. In particular, we show how to transform the efficient cryptographically secure Byzantine agreement protocol by Cachin, Kursawe and Shoup for the random oracle model into a cryptographically secure protocol for the complexity theoretic model without loosing efficiency or resilience, thereby constructing an efficient and optimally resilient Byzantine agreement protocol for the complexity theoretic model.