On Round-Efficient Argument Systems

Abstract

We consider the problem of constructing round-efficient public-coin argument systems, that is, interactive proof systems that are only computationally sound with a constant number of rounds. We focus on argument systems for NTime(T(n)) where either the communication complexity or the verifier’s running time is subpolynomial in T(n), such as Kilian’s argument system for NP [Kil92] and universal arguments [BG02,Mic00]. We begin with the observation that under standard complexity assumptions, such argument systems require at least 2 rounds. Next, we relate the existence of non-trivial 2-round argument systems to that of hard-on-average search problems in NP and that of efficient public-coin zero-knowledge arguments for NP. Finally, we show that the Fiat-Shamir paradigm [FS86] and Babai-Moran round reduction [BM88] fails to preserve computational soundness for some 3-round and 4-round argument systems.