Byzantine-Eavesdropper Alliance: How to Achieve Symmetric Privacy in Quantum $X$-Secure $B$-Byzantine $E$-Eavesdropped $U$-Unresponsive $T$-Colluding PIR?
Mohamed Nomeir, Alptug Aytekin, Sennur Ulukus
TL;DR
The work addresses quantum symmetric private information retrieval (QSPIR) with multiple threat models, notably dynamic eavesdroppers and Byzantine servers, in a setting with $N$ databases and $K$ messages. It introduces the $N$-sum box abstraction to design regime-based achievable schemes that jointly handle unresponsive servers, colluding servers, eavesdropper taps, and Byzantine behavior, achieving rate regions that leverage quantum coding and super-dense coding gains in several regimes. The paper provides concrete construction steps, noise masking strategies, and decoding procedures to ensure symmetric privacy and eavesdropper security, complemented by decoding methods for Byzantine errors. The results systematically quantify how dynamic eavesdroppers and Byzantine coordination degrade or can be mitigated, offering practical guidance for secure quantum PIR under complex threat models and highlighting the interplay between quantum resources and classical-like coding strategies. Overall, the work extends quantum PIR theory to richer adversarial models and delineates regime-dependent performance bounds with explicit transfer matrices and masking schemes.
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.