Maximizing randomness in ring oscillators for security applications

Existing works on generating random bits by ring oscillators (ROs) mostly do not have detailed analysis on phase noise and jitter which are the entropy source of a random number generator. This paper analyzes the suitability of existing ROs for random number generation and possible improvements in order to increase the randomness of a RO. Randomness equations are derived, to understand efficiency of these derivations, hand calculation and simulation results are compared. For this purpose, two cases are studied: Inverter-based Ring Oscillators (IbRO) and Differential Ring Oscillators (DROs). 0.35µm standard CMOS process has been used with a supply voltage of 3.3V for designs and analysis. For both ROs, randomness increases with decreasing energy. It is also observed that randomness of DRO does not have dependence on V
DD
as strong as in IbRO. Furthermore, for a given oscillation frequency, DRO exhibits 48 times more randomness than inverter-based one. Therefore, for random number applications, DRO is more suitable in terms of randomness that they produce.