Stationary Randomness of Quantum Cryptographic Sequences on Variant Maps

Abstract

Natural and artificial sequences of big data streams have various stationary and non-stationary properties. A Quantum Key Distribution (QKD) system has a quantum random number generator to protect data streams in quantum communication environments. From a cryptanalysis viewpoint, it is necessary to use statistical probability, stochastic processes and time series to evaluate quality of stationary randomness in quantum cryptographic sequrences. In this paper, a testing model is proposed to use statistical probability to illustrate multiple visual distributions on three maps for a selected random sequence. Under a shift operation to transfer the sequence into a shifted sequence, multiple segments are divided on the shifted sequence as three measuring sets to form three maps. For a given map, its maximal value is extracted from the distribution and three maximal values for the testing. Three 2D maps represent stationary random properties for the sequence under different shift operations. Conditions of station/stationary random sequences are investigated. Testing data sets are from two quantum cryptographic resources: Australian National University (ANU) and University of Science and Technology of China (USTC), two quantum cryptographic sequences are selected. Multiple results are created on three maps, and measurements of stationary randomness are illustrated. Using the testing system, measurements of stationary randomness are compared. There are only 0.07 ~ 0.27% variation differences identified among ANU and USTC samples for testing stationary randomness. Both samples show excellent stationary properties.