A cloud service to offer entropy has been paid much attention to. As one of the entropy sources, a physical random number generator is used as a true random number generator, relying on its irreproducibility. This paper focuses on a physical random number generator using a field-programmable gate array as an entropy source by employing ring oscillator circuits as a representative true random number generator. This paper investigates the effects of an XOR gate in the oscillation circuit by observing the output signal period. It aims to reveal the relationship between inputs and the output through the XOR gate in the target generator. The authors conduct two experiments to consider the relevance. It is confirmed that combining two ring oscillators with an XOR gate increases the complexity of the output cycle. In addition, verification using state transitions showed that the probability of the state transitions was evenly distributed by increasing the number of ring oscillator circuits.

A ring oscillator is a well-known circuit used for generating random numbers, and interested readers can find many research results concerning the evaluation of the randomness with a packaged test suit. However, the authors think there is room for evaluating the unpredictability of a sequence from another viewpoint. In this paper, the authors focus on Wold’s RO-based generator and propose a statistical test to numerically evaluate the randomness of the RO-based generator. The test adopts the state transition probabilities in a Markov process and is designed to check the uniformity of the probabilities based on hypothesis testing. As a result, it is found that the RO-based generator yields a biased output from the viewpoint of the transition probability if the number of ROs is small. More precisely, the transitions $01\to 01$ and $11\to 11$ happen frequently when the number l of ROs is less than or equal to 10. In this sense, $l>10$ is recommended for use in any application, though a packaged test suit is passed. Thus, the authors believe that the proposed test contributes to evaluating the unpredictability of a sequence when used together with available statistical test suits, such as NIST SP800-22.

This study examined the correlation between the number of delay flip-flops (D-FFs) connected after each ring oscillator (RO) and the bit distribution of random number sequences in an RO-based random number generator (RNG). In our previous research, unstable input signals to the XOR gate contributed to differences in bit distribution. Based on these results, we simulated how combining signals with biased distributions through XOR gates affects the overall bit distribution. Beyond this, we also conducted simulations where the inputs to the XOR gate included not just {0, 1} signals, but also three-state signals incorporating metastable states. We then proposed using multi-D-FFs as synchronization circuits for RO signals and performed analyses on RO-based RNG implementations by estimating metastable output conditions and conducting NIST Special Publication 800-22 tests regarding bit distributions. These results confirm that inserting two or more D-FFs after RO signals improves the bit distribution of RO-based RNG implementations.