Modelling 1/f Noise in TRNGs via Fractional Brownian Motion

Building upon the foundational work of atomic clock physicists Barnes and Allan, this paper presents a highly scalable and numerically exact framework for modeling \(1/f\) noise in oscillatory True Random Number Generators (TRNGs) and assessing their cryptographic security. By employing Fractional Brownian Motion, the framework constructs Gaussian non-stationary processes that represent these noise spectra accurately and in a mathematically sound way. Furthermore, it establishes several critical properties, including optimal bounds on the achievable generation rate of cryptographically secure bits.