Quantum Attacks on Classical Proof Systems - The Hardness of Quantum Rewinding (1404.6898v2)

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.

• The paper demonstrates classical proof systems, like Sigma-Protocols and Fiat-Shamir, are vulnerable to quantum attacks without strict soundness due to the hardness of quantum rewinding.
• The analysis shows the Fiat-Shamir construction fails to maintain security properties against quantum adversaries unless strict soundness is enforced.
• These findings highlight the critical need for developing quantum-resistant cryptographic protocols and moving beyond classical security assumptions.

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

This paper addresses a fundamental concern in quantum cryptography: the security of classical proof systems against quantum attacks. The authors provide an in-depth analysis of quantum rewinding, pivotal for understanding zero-knowledge proofs and proofs of knowledge in the quantum field. Despite advances laid by previous works, quantum rewinding remains a challenge due to inherent quantum properties, such as the no-cloning theorem.

Key Contributions

1. Sigma-Protocols: The paper demonstrates that sigma-protocols, classically considered secure, can become vulnerable in the quantum context without strict soundness. Through a meticulously constructed adversary model, the authors show that computationally securing sigma-protocols requires additional conditions when facing quantum-powered adversaries.
2. Fiat-Shamir Construction: A classical method to create non-interactive proofs, the Fiat-Shamir construction is analyzed rigorously. The paper establishes that while classically secure, the Fiat-Shamir method fails to ensure security and proof of knowledge properties when exposed to quantum adversaries, unless strict soundness is enforced.
3. Fischlin's Scheme: Despite Fischlin’s scheme not relying on rewinding for security proofs classically, the paper illustrates a total knowledge break against it. This surprising result signifies that quantum adversaries pose a substantial risk even to systems previously thought secure without rewinding.

Methodologies and Techniques

• Pick-One Trick: Central to the paper’s argument, the pick-one trick allows adversaries in the quantum setting to find one satisfying value efficiently but prevents them from finding multiple values required for extractability. It exposes weaknesses in classical assurance paradigms when they are transferred into quantum settings.
• State Creation Oracles: The paper develops theoretical constructs whereby quantum adversaries emulate state creation oracles. These constructs are foundational for understanding how quantum systems could interact with cryptographic protocols classically modeled.

Implications and Future Directions

The direct implications of these findings are twofold: confirming the necessity for non-relativizing proof techniques in quantum cryptographic security and incentivizing deeper exploration into quantum-secure protocol design. The results urge researchers to innovate beyond traditional cryptographic assumptions when considering quantum adversaries. It also opens avenues for exploring quantum-hard assumptions that do not rely on rewinding for zeroth-knowledge and proofs of knowledge.

Conclusion

"Quantum Attacks on Classical Proof Systems - The Hardness of Quantum Rewinding" delivers critical insights into the current vulnerabilities existing in classical cryptographic methods when faced with quantum technology. As quantum computing becomes more prevalent, the need for robust, quantum-resistant cryptographic protocols becomes more critical. The paper strongly contributes to the discourse, providing theoretical frameworks and examples where classical security paradigms require significant evolution. These discussions lay essential groundwork for future advancements in cryptographic constructs that stand resilient against the evolving quantum landscape.