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

The paper deals with true random number generators employing oscillator rings and 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 in their generator. 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 always let the statistical tests pass. We conclude that smaller number of rings reduces 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 more than 25 % of the rings are locked and thus completely dependent. This effect can have disastrous consequences on the security of the system.