Quantum Attacks on Classical Proof Systems - The Hardness of Quantum Rewinding
This work addresses a foundational problem in quantum cryptography by revealing inherent vulnerabilities in classical proof systems when faced with quantum adversaries, which is incremental but crucial for advancing secure quantum protocols.
The paper tackles the problem of analyzing quantum zero-knowledge proofs and proofs of knowledge by showing that classically secure proof systems, including sigma-protocols and the Fiat-Shamir construction, are insecure in the quantum setting relative to an oracle, and that computationally binding commitments provide minimal security guarantees under quantum attacks.
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.