On the Characterization of Jitter in Ring Oscillators using Allan variance for True Random Number Generator Applications

The description of the physical noise source is of utmost importance for any TRNG certification. In the case of ring oscillators, Allan variance is a reliable and comprehensive tool which enables the distinction between the jitter coming from flicker noise (autocorrelated) and from thermal noise (random). In this paper, we realize measurements directly on the analog source of numerous TRNG structures: a ring oscillator. Our data, along with evidence from the literature, indicates the presence of a third noise source. The quantization noise has not been so far taken into consideration, but is unquestionably present in all TRNG reliant on jitter. Its importance is key to an accurate estimation of thermal noise contribution, which can be shadowed by it. Measurements presented in this paper show that insufficient sampling (i.e. higher quantization noise) can lead to an overestimation of jitter coming from thermal noise and therefore an overestimation of the calculated entropy. The latter is the only type of noise considered reliable in currently existing ring oscillator-based TRNG models. As a rule of thumb, three orders of magnitude between the sampling and the sampled signal are necessary in order to determine the thermal noise jitter correctly.