Evaluation and Monitoring of Free Running Oscillators Serving as Source of Randomness

Abstract

In this paper, we evaluate clock signals generated in ring oscillators and self-timed rings and the way their jitter can be transformed into random numbers. We show that counting the periods of the jittery clock signal produces random numbers of significantly better quality than the methods in which the jittery signal is simply sampled (the case in almost all current methods). Moreover, we use the counter values to characterize and continuously monitor the source of randomness. However, instead of using the widely used statistical variance, we propose to use Allan variance to do so. There are two main advantages: Allan variance is insensitive to low frequency noises such as flicker noise that are known to be autocorrelated and significantly less circuitry is required for its computation than that used to compute commonly used variance. We also show that it is essential to use a differential principle of randomness extraction from the jitter based on the use of two identical oscillators to avoid autocorrelations originating from external and internal global jitter sources and that this fact is valid for both kinds of rings. Last but not least, we propose a method of statistical testing based on high order Markov model to show the reduced dependencies when the proposed randomness extraction is applied.

True random number generators with flicker noise: stochastic model, min-entropy calculation and online test

“…The device that we are modelling consists of two nominally identical oscillators [12]. The frequency of the first is divided by M to generate the slow clock.…”

“…which is essentially an estimator for the 2-sample Allan variance with equal time between measurements and measurement time, T = τ . It is easy to compute in real-time in digital circuits [12]. This quantity can be used to directly quantify the randomness properties of the oscillator.…”

“…In counting-mode oscillator TRNGs, one oscillator is used to generate the slow clock for a circuit that counts the periods of a second oscillator, using the least-significant bit (LSB) of the total count number in each period of the first oscillator as the random bit [10][11][12]. The simplest oscillators that can be implemented in CMOS technology or using programmable logic (FPGA) are elementary ring oscillators (EROs), chains of an odd number of NOT gates [13,14].…”

“…Ideally, only local random jitter would be used for random number generation. To filter out the global and deterministic noises, one typically uses differential configurations, where two nominally identical EROs are located in immediate vicinity on the chip [12], with the slow clock generated by frequency division of one of the two periodic signals. It is often assumed that the dominant contribution to jitter is the Johnson-Nyquist noise produced solely within the oscillators and that this noise is white (i.e., it has a spectrum that does not depend on the frequency).…”

Entropy Computation for Oscillator-based Physical Random Number Generators

“…We checked experimentally that the convergence is quicker when σ is bigger. To compute Table 1, we chose σ = 0.7 (which is in the order of typical values that we measure in real hardware implementations, see for example [1]) to be sure of making a realistic assessment of the convergence.…”