True-Randomness and Pseudo-Randomness in Ring Oscillator-Based True Random Number Generators

Abstract

The paper deals with true random number generators employing oscillator rings, namely, with the one proposed by Sunar et al. in 2007 and enhanced by Wold and Tan in 2009. Our mathematical analysis shows that both architectures behave identically when composed of the same number of rings and ideal logic components. However, the reduction of the number of rings, as proposed by Wold and Tan, would inevitably cause the loss of entropy. Unfortunately, this entropy insufficiency is masked by the pseudo-randomness caused by XOR-ing clock signals having different frequencies. Our simulation model shows that the generator, using more than 18 ideal jitter-free rings having slightly different frequencies and producing only pseudo-randomness, will let the statistical tests pass. We conclude that a smaller number of rings reduce the security if the entropy reduction is not taken into account in post-processing. Moreover, the designer cannot avoid that some of rings will have the same frequency, which will cause another loss of entropy. In order to confirm this, we show how the attacker can reach a state where over 25% of the rings are locked and thus completely dependent. This effect can have disastrous consequences on the system security.

A Very High Speed True Random Number Generator with Entropy Assessment

“…In contrast, the ring oscillator output signals from [7] drift in time and generate pseudo-randomness. This behavior was confirmed by simulations: sequences generated by combining signals from the outputs of 18 ideal inverters (without jitter) oscillating at slightly different frequencies, passed NIST statistical tests ( [12]). …”

A survey of AIS-20/31 compliant TRNG cores suitable for FPGA devices

“…4), which resolved the problems concerning the speed of the XOR gate. Since the authors of [25] proved that the stochastic model remains valid, we used this modified MURO-TRNG architecture in our study.…”

A Self-Timed Ring Based True Random Number Generator

“…Nonetheless, the proposed design have been also one of the most commented by the cryptographic community. Authors of [6] remark that the generator relies mostly on the pseudo-randomness which is introduced by the phase drift between the oscillators. They demonstrate this fact using digital simulations: they show that the combined signal issued from 18 ring oscillators having slight frequency differences passes FIPS and NIST statistical tests without incorporating jitter in their simulations.…”

“…In fact, a full independence of rings implemented in the same single logic device is a theoretical construct that is not generally achieved in real devices. Authors of [6] show that up to 25% of a set of 118 ring oscillators can be mutually locked in an Altera Cyclone III device. If the rings are not fully independent, their mutual phases cannot be uniformly distributed, which causes a lack of entropy at the output of the TRNG.…”