Boolean matrix multiplication (BMM) is a fundamental problem with applications in graph theory, group testing, data compression, and digital signal processing (DSP). The search for efficient BMM algorithms has produced several fast, albeit impractical, algorithms with sub-cubic time complexity. In this paper, we propose a memristor-crossbar framework for computing BMM at the hardware level in linear time. Our design leverages the diode-like characteristics of recently studied rectifying memristors to resolve the pervasive sneak paths constraint that is ubiquitous in crossbar computing.