Research on cryptographical properties of the piecewise linear chaotic map with a segment number parameter

Recently a new piecewise linear chaotic map (PLCM) with a segment number parameter (SNP) has been proposed. Its cryptographical properties including sensitivity to initial point and randomness of sequences obtained by iterating are very valuable in designing cryptosystems. The properties of digital PLCM with SNP are different from the continuous ones. In this paper, these cryptographical properties were analyzed when the map was realized in finite computing precision. The functional relationship among SNP, implementation precision, the number of iterating was developed in order for sensitivity to initial point; the statistical properties were also investigated. The analysis result will be valuable for the research on chaotic cryptography.