Cryptology ePrint Archive: Report 2014/296

Quantum Attacks on Classical Proof Systems - The Hardness of Quantum Rewinding

Andris Ambainis and Ansis Rosmanis and Dominique Unruh

Abstract: Quantum zero-knowledge proofs and quantum proofs of knowledge are inherently difficult to analyze because their security analysis uses rewinding. Certain cases of quantum rewinding are handled by the results by Watrous (SIAM J Comput, 2009) and Unruh (Eurocrypt 2012), yet in general the problem remains elusive. We show that this is not only due to a lack of proof techniques: relative to an oracle, we show that classically secure proofs and proofs of knowledge are insecure in the quantum setting.

More specifically, sigma-protocols, the Fiat-Shamir construction, and Fischlin's proof system are quantum insecure under assumptions that are sufficient for classical security. Additionally, we show that for similar reasons, computationally binding commitments provide almost no security guarantees in a quantum setting.

To show these results, we develop the "pick-one trick", a general technique that allows an adversary to find one value satisfying a given predicate, but not two.

Category / Keywords: foundations / Quantum cryptography, proofs of knowledge, rewinding, random oracles

Original Publication (with major differences): FOCS 2014

Date: received 28 Apr 2014, last revised 19 Oct 2014

Contact author: unruh at ut ee

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Version: 20141019:134739 (All versions of this report)

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