Access control is a foundation of security and is implemented in the hardware of Systems-on-chip. The entire system stack relies on the secure and correct functioning of these access control mechanisms. However, contemporary security verification methods face major challenges in exhaustively detecting targeted security vulnerabilities while also being scalable. We address these challenges with a novel formulation of security property sets. Our approach introduces interlocked property sets, which have a mathematical characteristic that enables scalable and exhaustive verification of general security targets. We propose an interlocked property set for access control verification in processors and have evaluated our approach in several case studies on RISC-V processor cores. Our approach detected multiple security vulnerabilities.