Private information retrieval (PIR) allows a client to query a public database privately and serves as a key building block for privacy-enhancing applications. Minimizing query size is particularly important in many use cases, for example, when clients operate on bandwidth-constrained devices. However, existing PIR protocols exhibit large query sizes: to query 225 records, the smallest query size of 14.8 KB is reported in Respire [Burton et al., CCS24]. Respire is based on fully homomorphic encryption (FHE), where a common approach to lower the client-to-server communication cost is transciphering. When combining the state-of-the-art transciphering [Bon et al., CHES24] with Respire, the resulting protocol (which we refer to as T-Respire) has a 336 B query size, while incurring a 16.2x times higher server computation cost than Respire. Our work introduces a novel alternative to transciphering for reducing the client-to-server communication: the client transmits only one component of a high-precision LWE ciphertext, from which we design a modular procedure to extract the inputs for the subsequent homomorphic computation. The efficiency of this approach is demonstrated by our Pirouette protocol, which achieves a query size of just 36 B. This represents a 9.3x reduction compared to T-Respire and a 420x reduction to Respire. For queries over 225 records, the single-core server computation in Pirouette is only 2x slower than Respire and 8.1x faster than T-Respire, and the server computation is highly parallelizable. Furthermore, Pirouette requires no database-specific hint for clients, and its variant PirouetteH enables additional tradeoffs among query size, throughput, and offline communication, demonstrating the flexibility of our design

In this article, we propose the novel neural stochastic differential equations (SDEs) driven by noisy sequential observations called neural projection filter (NPF) under the continuous state-space models (SSMs) framework. The contributions of this work are both theoretical and algorithmic. On the one hand, we investigate the approximation capacity of the NPF, i.e., the universal approximation theorem for NPF. More explicitly, under some natural assumptions, we prove that the solution of the SDE driven by the semimartingale can be well approximated by the solution of the NPF. In particular, the explicit estimation bound is given. On the other hand, as an important application of this result, we develop a novel data-driven filter based on NPF. Also, under certain condition, we prove the algorithm convergence; i.e., the dynamics of NPF converges to the target dynamics. At last, we systematically compare the NPF with the existing filters. We verify the convergence theorem in linear case and experimentally demonstrate that the NPF outperforms existing filters in nonlinear case with robustness and efficiency. Furthermore, NPF could handle high-dimensional systems in real-time manner, even for the 100-D cubic sensor, while the state-of-the-art (SOTA) filter fails to do it.