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.
Bounds on Fixed Input/Output Length Post-processing Functions for Biased Physical Random Number Generators