We propose and study a new privacy definition, termed Probably Approximately Correct (PAC) Security. PAC security characterizes the information-theoretic hardness to recover sensitive data given arbitrary information disclosure/leakage during/after any processing. Unlike the classic cryptographic definition and Differential Privacy (DP), which consider the adversarial (input-independent) worst case, PAC security is a simulatable metric that quantifies the instance-based impossibility of inference. A fully automatic analysis and proof generation framework is proposed: security parameters can be produced with arbitrarily high confidence via Monte-Carlo simulation for any black-box data processing oracle. This appealing automation property enables analysis of complicated data processing, where the worst-case proof in the classic privacy regime could be loose or even intractable. Moreover, we show that the produced PAC security guarantees enjoy simple composition bounds and the automatic analysis framework can be implemented in an online fashion to analyze the composite PAC security loss even under correlated randomness. On the utility side, the magnitude of (necessary) perturbation required in PAC security is not lower bounded by Theta(\sqrt{d}) for a d-dimensional release but could be O(1) for many practical data processing tasks, which is in contrast to the input-independent worst-case information-theoretic lower bound. Example applications of PAC security are included with comparisons to existing works.

翻译：我们提出并研究了一种新的隐私定义，称为“近似正确安全”（Probably Approximately Correct Security, PAC Security）。PAC安全刻画了在任意处理过程中或处理后，给定任意信息泄露时，恢复敏感数据的信息论难度。与经典的密码学定义和差分隐私（Differential Privacy, DP）考虑对抗性（输入无关的）最坏情况不同，PAC安全是一种可模拟的度量，用于量化基于实例的推理不可行性。我们提出了一种全自动的分析与证明生成框架：通过蒙特卡洛模拟，对于任意黑盒数据处理预言机，可以以任意高的置信度生成安全参数。这种吸引人的自动化特性使得对复杂数据处理的隐私分析成为可能，而在经典隐私体制中，最坏情况下的证明可能过于宽松甚至难以处理。此外，我们证明了所生成的PAC安全保证具有简单的组合界，并且该自动分析框架可以在线实现，即使在相关随机性下也能分析组合PAC安全损失。在效用方面，PAC安全所需（必要）扰动的幅度对于d维发布并非以Theta(√d)为下界，对于许多实际数据处理任务而言可能仅为O(1)，这与输入无关最坏情况下的信息论下界形成对比。本文还包含了PAC安全的示例应用及与现有工作的比较。