Minimum resource zero-knowledge proofs

Abstract

What are the resources of a zero-knowledge Proof? Interaction, communication, and en- velops. That interaction, that is the number of rounds of a protocol, is a resource is clear. Actually, it is not a very available one: having someone on the line to answer your questions all the time is quite a luxury. Thus, minimizing the number of rounds in zero-knowledge proofs will make these proofs much more attractive from a practical standpoint. That communication, that is the number of bits exchanged in a protocol, is a resource is also immediately clear. Perhaps, what is less clear is why envelopes are a resource. Let us explain why this is the case.