Unpredictability and robustness of chaotic dynamics for physical random number generation

Abstract

Random number generation is a fundamental technology behind information security. Recently, physical random number generators (RNGs), which especially harness optical chaos such as in delay-feedback lasers, have been studied intensively. Although these are promising technologies for future information security, there is little theoretical foundation. In this paper, we newly introduce a mathematical formulation of physical RNGs based on a model of chaotic dynamics and give the first rigorous results. In particular, by combining ergodic theory, information theory, and response theory of statistical physics, our theory guarantees, for the model of chaotic dynamics, the coexistence of two crucial properties necessary for physical RNGs: fast random number generation and robustness. Compared with other types of physical RNGs, our theoretical findings highlight an unnoticed advantage of chaotic dynamics utilized for physical RNGs.