Mathematical model of physical RNGS based on coherent sampling

Abstract

ABSTRACT. 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.