True random number generators (TRNGs) are crucial to the implementations of cryptographic algorithms and protocols. The quality of randomness directly influences the security of cryptographic systems. Oscillator-based sampling is popular in the design of TRNGs due to its nice properties of elegant structure and high speed. However, the credibility of randomness generated from high-speed oscillator-based TRNGs, especially ring oscillator-based (RO-based) ones, is still in controversy. This is mainly because pseudo-randomness is hardly distinguished from true randomness and RO-based TRNGs are susceptible to external perturbations. In this paper, we present a stochastic model to evaluate the entropy of oscillator-based TRNGs, and then deduce the requirement of design parameters (including the sampling interval) for sufficient entropy per random bit, i.e., to ensure true randomness. Furthermore, we design a jitter measuring circuit to verify the theory, and the theoretical results are confirmed by both the simulation and practical experiments. Finally, e apply the stochastic model to analyze the effect of deterministic perturbations, and demonstrate that the randomness of RO-based TRNGs (under deterministic perturbations) can be overestimated and predicting the random bits could be possible. © International Association for Cryptologic Research 2014.