On Entropy and Bit Patterns of Ring Oscillator Jitter

Thermal jitter (phase noise) from a free-running ring oscillator is a common, easily implementable physical randomness source in True Random Number Generators (TRNGs). We show how to evaluate entropy, autocorrelation, and bit pattern distributions of such entropy sources, even when they have low jitter levels or some bias. Our numerical evaluation algorithms vastly outperform simple Monte Carlo simulations in speed and accuracy. This helps in choosing the most appropriate parameters for TRNG self-tests and cryptographic post-processing. We also propose a new, safer lower bound estimation formula for the entropy of such randomness sources.