Mathematical model of physical RNGs based on coherent sampling

Random number generators represent one of basic cryptographic primitives used in creating cryptographic protocols. Their security evaluation represents very important part in the design, implementation and employment phase of the generator. One of important security requirements is the existence of a mathematical model describing the physical noise source and the statistical properties of the digitized noise derived from it. The aim of this paper is to propose the model of a class of generators using two jittery clocks with rationally related frequencies. The clock signals with related frequencies can be obtained using phase-locked loops, delay-locked loops or ring oscillators with adjusted oscillation periods. The proposed mathematical model is used to provide entropy per bit estimators and expected bias on the generated sequence. The model is validated by hardware experiments.