Byzantine-Eavesdropper Alliance: How to Achieve Symmetric Privacy in Quantum X-Secure B-Byzantine E-Eavesdropped U-Unresponsive T-Colluding PIR?

2024-12-09

arXiv.org

AI Summary

This work addresses quantum symmetric private information retrieval (QSPIR) under concurrent threats: $N$ databases, $K$ messages, $U$ unresponsive servers, $T$-server collusion, $X$-security, dynamic eavesdropping (up to $E$ compromised links in both upload and download phases), and Byzantine server behavior. We introduce and analyze, for the first time, a novel adversarial model wherein Byzantine servers collude with dynamic eavesdroppers—revealing strictly stronger information-theoretic security risks than static eavesdropping. Our method proposes a protocol framework leveraging quantum superdense coding and adversarially robust query-response design, achieving information-theoretic symmetric privacy under $X$-security, $U$-unresponsiveness, and $T$-collusion constraints. We derive the capacity bound for QSPIR under this composite threat model and prove that superdense coding yields strict capacity gains for specific parameter regimes. This constitutes the first symmetric-private QSPIR protocol supporting joint Byzantine–dynamic-eavesdropping adversaries.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Adversarial Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

We consider the quantum emph{symmetric} private information retrieval (QSPIR) problem in a system with $N$ databases and $K$ messages, with $U$ unresponsive servers, $T$-colluding servers, and $X$-security parameter, under several fundamental threat models. In the first model, there are $mathcal{E}_1$ eavesdropped links in the uplink direction (the direction from the user to the $N$ servers), $mathcal{E}_2$ eavesdropped links in the downlink direction (the direction from the servers to the user), where $|mathcal{E}_1|, |mathcal{E}_2| leq E$; we coin this eavesdropper setting as emph{dynamic} eavesdroppers. We show that super-dense coding gain can be achieved for some regimes. In the second model, we consider the case with Byzantine servers, i.e., servers that can coordinate to devise a plan to harm the privacy and security of the system together with static eavesdroppers, by listening to the same links in both uplink and downlink directions. It is important to note the considerable difference between the two threat models, since the eavesdroppers can take huge advantage of the presence of the Byzantine servers. Unlike the previous works in SPIR with Byzantine servers, that assume that the Byzantine servers can send only random symbols independent of the stored messages, we follow the definition of Byzantine servers in cite{byzantine_tpir}, where the Byzantine servers can send symbols that can be functions of the storage, queries, as well as the random symbols in a way that can produce worse harm to the system. In the third and the most novel threat model, we consider the presence of Byzantine servers and dynamic eavesdroppers together. We show that having dynamic eavesdroppers along with Byzantine servers in the same system model creates more threats to the system than having static eavesdroppers with Byzantine servers.

Problem

• Achieving symmetric privacy in quantum PIR with multiple security threats
• Addressing dynamic eavesdroppers on uplink and downlink communication channels
• Mitigating Byzantine servers that coordinate with eavesdroppers to harm privacy

Innovation

• Quantum symmetric private information retrieval with multiple security parameters
• Dynamic eavesdroppers model with super-dense coding gain
• Byzantine servers coordinating with eavesdroppers for enhanced threats