Differential privacy (DP) has a wide range of applications for protecting data privacy, but designing and verifying DP algorithms requires expert-level reasoning, creating a high barrier for non-expert practitioners. Prior works either rely on specialized verification languages that demand substantial domain expertise or remain semi-automated and require human-in-the-loop guidance. In this work, we investigate whether large language models (LLMs) can automate DP reasoning. We introduce DPrivBench, a benchmark in which each instance asks whether a function or algorithm satisfies a stated DP guarantee under specified assumptions. The benchmark is carefully designed to cover a broad range of DP topics, span diverse difficulty levels, and resist shortcut reasoning through trivial pattern matching. Experiments show that while the strongest models handle textbook mechanisms well, all models struggle with advanced algorithms, revealing substantial gaps in current DP reasoning capabilities. Through further analytic study and failure-mode analysis, we identify several promising directions for improving automated DP reasoning. Our benchmark provides a solid foundation for developing and evaluating such methods, and complements existing benchmarks for mathematical reasoning.

翻译：差分隐私（DP）在保护数据隐私方面具有广泛应用，但设计与验证DP算法需要专家级推理能力，为不具备专业知识的从业者设置了较高门槛。现有研究要么依赖需深厚领域知识的专用验证语言，要么仍停留在半自动化阶段并需要人工持续引导。本研究探讨大语言模型（LLMs）能否实现DP推理的自动化。我们提出DPrivBench基准测试，其中每个实例要求判断函数或算法在给定假设下是否满足指定DP保证。该基准测试精心设计，涵盖广泛的DP主题、跨越多层次难度等级，并通过避免琐碎模式匹配来抵御捷径推理。实验表明，尽管最强模型能较好处理教科书级机制，但所有模型在处理高级算法时均存在困难，揭示了当前DP推理能力的显著缺陷。通过进一步分析研究与失效模式剖析，我们识别出改进自动化DP推理的若干潜在方向。本基准测试为开发与评估此类方法奠定了坚实基础，并可作为对现有数学推理基准测试的补充。