We show that if any one-way function exists, then 3-round concurrent zero-knowledge arguments for all NP problems can be built in a model where a short auxiliary string with a pres...
Abstract. We present a lower bound on the number of rounds required by Concurrent Zero-Knowledge proofs for languages in NP. It is shown that in the context of Concurrent Zero-Know...
We show that every language in NP has a (black-box) concurrent zero-knowledge proof system using ˜O(log n) rounds of interaction. The number of rounds in our protocol is optimal,...