Looking for suitable rules for true random number generation with asynchronous cellular automata

Achieving true random behavior in digital systems represents both a challenge and an opportunity for high-performance true random number generation (TRNG). Asynchronous cellular automata (ACA) are interesting candidates for reconfigurable hardware implementations, but one of its main problems is the identification of the best rules for performance and quality. In this article, we propose an analytical approach to evaluate and select suitable rules for TRNG with physical implementations of ACA networks. We introduce the concept of rule reactivity as an indicator of the expected ACA average transition rate. We also propose the concept of rule disequilibrium function for probabilistic estimation of the ACA output balance. Based on these analytic tools, it is possible to identify the best rules for ACA with any number of inputs.