Behavioral model of TRNG based on oscillator rings implemented in FPGA

Understanding the behavior of a true random number generator (TRNG) is important in order to determine the security of such a design. In this paper, an investigation of a TRNG design based on several oscillator rings implemented in a field programmable gate array (FPGA) is performed in order to determine the amount of true randomness or entropy in this design. A model of the TRNG based on the number of hits in the transition regions generating entropy is proposed. This model takes into account the fact that the jitter of an oscillator ring is not constant, but increases or accumulates if the ring is not sampled in a region close to a transition point where the oscillator ring output changes from logic 0 to logic 1 or vice versa. The model of the TRNG is implemented in MatLab and simulations are performed showing the influence of different design parameters and also the influence of properties of the FPGA device on quality of randomness.