[Paper Review] Privacy Amplification Against Active Quantum Adversaries

Gil Cohen, Thomas Vidick|arXiv (Cornell University)|Aug 22, 2016

Cryptography and Data Security26 references3 citations

TL;DR

This paper presents the first privacy amplification protocol secure against active quantum adversaries by proving the security of the Dodis-Wichs two-message protocol when its non-malleable extractor component is quantum-proof. It introduces quantum-proof non-malleable extractors and shows that an adaptation of a recent construction by Chattopadhyay et al. satisfies this property, enabling information-theoretic security against quantum side information.

ABSTRACT

Privacy amplification is the task by which two cooperating parties transform a shared weak secret, about which an eavesdropper may have side information, into a uniformly random string uncorrelated from the eavesdropper. Privacy amplification against passive adversaries, where it is assumed that the communication is over a public but authenticated channel, can be achieved in the presence of classical as well as quantum side information by a single-message protocol based on strong extractors. In 2009 Dodis and Wichs devised a two-message protocol to achieve privacy amplification against active adversaries, where the public communication channel is no longer assumed to be authenticated, through the use of a strengthening of strong extractors called non-malleable extractors which they introduced. Dodis and Wichs only analyzed the case of classical side information. We consider the task of privacy amplification against active adversaries with quantum side information. Our main result is showing that the Dodis-Wichs protocol remains secure in this scenario provided its main building block, the non-malleable extractor, satisfies a notion of quantum-proof non-malleability which we introduce. We show that an adaptation of a recent construction of non-malleable extractors due to Chattopadhyay et al. is quantum proof, thereby providing the first protocol for privacy amplification that is secure against active quantum adversaries. Our protocol is quantitatively comparable to the near-optimal protocols known in the classical setting.

Motivation & Objective

• Address the gap in privacy amplification protocols that are secure against active adversaries when the eavesdropper has quantum side information.
• Extend the Dodis-Wichs two-message protocol—originally designed for classical side information—to the quantum setting.
• Introduce and formalize the notion of quantum-proof non-malleable extractors as a necessary building block for security in the quantum adversary model.
• Demonstrate that a recent construction of non-malleable extractors by Chattopadhyay et al. is quantum-proof, thereby enabling the first secure protocol in this setting.
• Achieve a protocol with quantitative efficiency comparable to near-optimal classical protocols, ensuring practical relevance.

Proposed method

• Adapt the two-message protocol of Dodis and Wichs for active adversaries to the quantum setting by ensuring its core component, the non-malleable extractor, is quantum-proof.
• Introduce the concept of quantum-proof non-malleable extractors, which must remain secure even when the adversary holds quantum side information.
• Prove that a recent construction of non-malleable extractors by Chattopadhyay et al. satisfies the quantum-proof non-malleability condition.
• Use the security of the non-malleable extractor under quantum attacks to establish the overall security of the privacy amplification protocol.
• Leverage the properties of strong extractors and their strengthening to non-malleable extractors to ensure resilience against active tampering and quantum side information.
• Analyze the protocol’s security using information-theoretic techniques, showing that the output string remains uniformly random and uncorrelated from the adversary’s quantum system.

Experimental results

Research questions

• RQ1 Can the Dodis-Wichs two-message privacy amplification protocol be extended to remain secure when the adversary has quantum side information?
• RQ2 What additional properties must a non-malleable extractor satisfy to ensure security in the presence of quantum adversaries?
• RQ3 Is there a known construction of non-malleable extractors that satisfies the newly introduced notion of quantum-proof non-malleability?
• RQ4 Can a quantum-secure protocol for privacy amplification be constructed with efficiency comparable to classical near-optimal protocols?
• RQ5 What is the minimal assumption on the adversary’s capabilities that still allows for information-theoretic security in the active quantum setting?

Key findings

• The Dodis-Wichs two-message protocol remains secure against active adversaries when the non-malleable extractor used is quantum-proof.
• The notion of quantum-proof non-malleable extractors is formally defined and shown to be sufficient for security in the quantum adversary model.
• An adaptation of the non-malleable extractor construction by Chattopadhyay et al. is proven to be quantum-proof, providing a concrete instantiation.
• The resulting protocol achieves information-theoretic security against active quantum adversaries, marking the first such protocol in this setting.
• The protocol’s efficiency is quantitatively comparable to near-optimal classical protocols, indicating strong practical feasibility.
• The security proof relies on information-theoretic techniques and holds even when the adversary controls the public channel and holds quantum side information.