Correlative Peak Interval Prediction and Analysis of Chaotic Sequences

The paper proposes a digital circuit design for the logistic-map module used in chaotic stream ciphers, analyzes the factors that may affect the output of the sequences, and develops a calculation method for estimating the output sequential correlative peak interval. With the respective tests using different initial values, the values of parameter u and the computational precisions, extensive experiments have been carried out. A formula for calculating correlative peak interval is proposed. Moreover, the relationships among precision, parameter u and correlative peak interval is provided. To ensure the security of the plaintext which is encrypted by the output sequence of the logistic-map, a proper precision could be chosen according to the formula. It provides a theoretic basis for the actual application of the chaos cryptology. The basic theory and methods have a significant implication on the statistical analysis and practical applications of the digital chaotic sequences. A diagram that presents the relationship among precision, parameter u and correlative peak interval has been generated for analysis.