This project will support research that contributes novel methodologies related to privacy protection of multi-robot systems, promoting the progress of science and advancing national health and prosperity. Due to possible active and passive intruders who may gain access to communication channels and observe the system behaviors, private information can be leaked through robot behaviors. However, existing works on privacy analysis of robot behaviors may not scale when the system dimension increases. This project supports fundamental research that addresses the major challenges in multi-robot systems, privacy analysis, algorithm design, computation, and information theory. The project will contribute to more secure and private robotic systems and increase the usage of robots in various domains to increase efficiency and safety. Existing approaches on privacy analysis of robot behaviors rely on the construction of a deterministic observer, and therefore require an exponential complexity for privacy analysis. To address this, this project will develop a scalable computation framework for analyzing behavior privacy of multi-robot systems, which reduces the computation complexity with quantifiable and acceptable error bounds. Four closely integrated research objectives are planned: (1) Develop a scalable privacy verification framework with only polynomial complexity to verify that there is no privacy leak; (2) Develop a scalable privacy quantification framework to measure the ro