Zero-knowledge against quantum attacks

It is proved that several interactive proof systems are zero-knowledge against general quantum attacks. This includes the Goldreich?Micali?Wigderson classical zero-knowledge protocols for Graph Isomorphism and Graph 3-Coloring (assuming the existence of quantum computationally concealing commitment schemes in the second case). Also included is a quantum interactive proof system for a complete problem for the complexity class of problems having honest verifier quantum statistical zero-knowledge proofs, which therefore establishes that honest verifier and general quantum statistical zero-knowledge are equal: QSZK = QSZKHV. Previously no non-trivial interactive 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.

• Type: Conference
• Year: 2006
• Where: STOC
• Authors: John Watrous
• Keywords: Algorithms, Common Reference String, Interactive Proof Systems, Quantum Statistical Zero-knowledge, STOC 2006