In traditional runtime verification, a system is typically observed by a monolithic monitor. Enforcing privacy in such settings is computationally expensive, as it necessitates heavy cryptographic primitives. Therefore, privacy-preserving monitoring remains impractical for real-time applications. In this work, we address this scalability challenge by distributing the monitor across multiple parties -- at least one of which is honest. This architecture enables the use of efficient secret-sharing schemes instead of computationally intensive cryptography, dramatically reducing over-head while maintaining strong privacy guarantees. While existing secret-sharing approaches are typically limited to one-shot executions which do not maintain an internal state, we introduce a protocol tailored for continuous monitoring that supports repeated evaluations over an evolving internal state (kept secret from the system and the monitoring entities). We implement our approach using the MP-SPDZ framework. Our experiments demonstrate that, under these architectural assumptions, our protocol is significantly more scalable than existing alternatives.

翻译：在传统的运行时验证中，系统通常由单一监控器进行观测。在此类设置中实施隐私保护计算成本高昂，因为必须借助繁重的密码学原语。因此，隐私保护监控在实时应用中仍不实用。在本研究中，我们通过将监控器分布在多个参与方之间（其中至少一方是诚实的）来解决这一可扩展性挑战。该架构使得我们能够使用高效的秘密共享方案替代计算密集型的密码学方法，在维持强隐私保障的同时大幅降低开销。针对现有秘密共享方法通常局限于不维护内部状态的一次性执行这一局限，我们引入了一种专为持续监控设计的协议，该协议支持基于持续演化的内部状态（对系统和监控实体保密）进行重复评估。我们使用MP-SPDZ框架实现了所提出的方案。实验表明，在所述架构假设下，我们的协议在可扩展性方面显著优于现有替代方案。