We obtain new $\mathsf{NC}^1$-computable pseudorandom functions (PRFs) from various standard assumptions, resolving several long-standing open problems. Concretely, for the first time, we obtain $\mathsf{NC}^1$-computable PRFs: (1) from the \textbf{Learning With Errors (LWE)} assumption with a polynomial modulus-to-noise ratio, improving upon prior low-depth constructions that required Ring-LWE with super-polynomial ratios [Banerjee-Peikert-Rosen, EUROCRYPT 2012]; (2) from the \textbf{Learning Parity with Noise (LPN)} assumption, removing the need for structured LPN variants [Boyle et al., FOCS 2020], [Ding-Jain-Komargodski, STOC 2025], [Ding-Jain-Komargodski, TCC 2026]; (3) from the \textbf{Computational Diffie-Hellman (CDH)} assumption; prior works relied on the stronger Decisional Diffie-Hellman (DDH) or generalized Diffie-Hellman (GDH) assumptions [Naor-Reingold, FOCS '97, J. ACM '04]. Technically, our results follow from a new generic transformation that converts weak PRFs computable in depth $d(n) = Ω(\log n)$ to (strong) PRFs computable in depth $O(d(n))$. Roughly speaking, our approach combines \emph{tapering} the internal state of the classical GGM tree (so that the per-leveldepth decreases geometrically) with a two-stage security proof that transitions from a computational to an information-theoretic argument.
Peihua Mai, Xuanrong Gao, Youlong Ding Hebrew University of Jerusalem, Xianglong Du Changan Automobile, Wei Liu Changan Automobile, Yan Pang National University of Singapore
With the widespread deployment of public large language models (LLMs) such as ChatGPT, protecting user prompt privacy has become an increasingly critical issue. Existing privacy-preserving inference methods sacrifice either utility or efficiency, and often require model-specific modifications that limit their compatibility. In this paper, we propose SharedRequest, a model-agnostic framework for privacy-preserving LLM inference that reformulates privacy protection at the batch level rather than the individual-prompt level. The key idea is to obscure sensitive information by mixing original prompts with noisy variants, while grouping semantically equivalent instructions to amortize the inference cost over a large batch of queries with minimal impact on LLM response quality. This design is independent of the LLM architecture, requiring no access to model parameters or architectural modification. Empirical results demonstrate that SharedRequest achieves over 20% higher utility compared to prior differential privacy baselines, and its shared-prompt mechanism reduces query cost by up to 5\times compared to non-batched inference.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表