Zero-knowledge against quantum attacks

Abstract

This paper proves that several interactive proof systems are zero-knowledge against quantum attacks. This includes a few well-known classical zero-knowledge proof systems as well as quantum interactive proof systems for the complexity class HVQSZK, which comprises all problems having "honest verifier" quantum statistical zero-knowledge proofs. It is also proved that zero-knowledge proofs for every language in NP exist that are secure against quantum attacks, assuming the existence of quantum computationally concealing commitment schemes. Previously no non-trivial proof systems were known to be zero-knowledge against quantum attacks, except in restricted settings such as the honest-verifier and common reference string models. This paper therefore establishes for the first time that true zero-knowledge is indeed possible in the presence of quantum information and computation.