Generating randomness from chaos and constructing chaos with desired randomness

摘要

AbstractWe have designed, built and tested a switched‐capacitor circuit for generating pseudo‐random signals. the circuit is an electronic implementation of a one‐dimensional discrete map, which has been fully understood mathematically. the time series of the circuit has extremely rich dynamics, e.g. aperiodicity, non‐asymptoticity, ergodicity and fractal dimension. That is, the circuit is indeed chaotic. Furthermore, a general method for designing chaotic circuits with prescribed random properties is proposed. Numerous examples are given to illustrate the theory and methods developed in thi