Privacy-Preserving Robust Monitoring of Dense-Time Temporal Logic

Abstract

Motivated by the use of third-party testing, this paper presents a privacy-preserving implementation of the robustness monitoring of Signal Temporal Logic (STL). STL is a specification language for systems whose output traces have real-valued timestamps – most prominently, cyber-physical systems. Its robust semantics, which assign real rather than binary truth values, are an essential ingredient of systems testing and runtime monitoring. In a number of system testing scenarios, the designer and the tester are separate parties. This testing-as-a-service model is common in software, avionics, and semiconductors, and is growing in importance in the red-teaming of machine learning models. In such a model, the designer seeks to preserve the privacy (or secrecy) of its design, while the tester seeks to preserve the privacy of its collateral, including the detailed specification suite. This paper presents a secure multi-party implementation of the robust semantics using arithmetic circuits. This implementation allows one party, which provides a secret trace, and a second party which provides a secret formula, to jointly compute the robustness without either party being able to learn the other party’s secret input. We present a number of algorithmic modifications to the robustness computation to enable an efficient multi-party robustness computation. We also present new, semi-linear, robust semantics for STL that take advantage of the efficiencies of arithmetic circuits. The experimental results demonstrate that not only is this privacy-preserving monitor efficient on its own, but also that it can be used in a testing loop without affecting the speed at which bugs are found during robustness-guided system testing.