@MISC{Bitansky12succinctarguments, author = {Nir Bitansky and Alessandro Chiesa}, title = {Succinct arguments from . . . }, year = {2012} }

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Abstract

Succinct arguments of knowledge are computationally-sound proofs of knowledge for NP where the verifier’s running time is independent of the time complexity t of the nondeterministic NP machine M that decides the given language. Existing succinct argument constructions are, typically, based on techniques that combine cryptographic hashing and probabilistically-checkable proofs (PCPs). Yet, even when instantiating these constructions with state-of-the-art PCPs, the prover needs Ω(t) space in order to run in quasilinear time (i.e., time t · poly(k)), regardless of the space complexity s of the machine M. We say that a succinct argument is complexity preserving if the prover runs in time t · poly(k) and space s · poly(k) and the verifier runs in time |x | · poly(k) when proving and verifying that a t-time s-space random-access machine nondeterministically accepts an input x. Do complexity-preserving succinct arguments exist? To study this question, we investigate the alternative approach of constructing succinct arguments based on multi-prover interactive proofs (MIPs) and stronger cryptographic techniques: (1) We construct a one-round succinct MIP of knowledge, where each prover runs in time t · polylog(t) and space s · polylog(t) and the verifier runs in time |x | · polylog(t). (2) We show how to transform any one-round MIP protocol to a succinct four-message argument (with