The Study, Based On Floating-point Format Of The Digital Chaotic System Cycle

The periods and their distribution of a digital chaotic system, essential content of chaotic degradation and anti-degradation mechanism research, is an important indicator of assessing the capacity of anti-dagradation and the safety of a chaotic encryption algorithm. The existing conclusions about empirical relation of 1-D chaotic system's average period and the distribution range of periods are all based on fix-point formats. If using them as the quantitative assessment criteria of chaotic anti-dagration, theoretical basis is not sufficient.To get an empirical relation with more theoretical and applicative value, the periods and their distribution of digital chaotic systems based on floating-point formats are studied in this paper. Because standard floating-point formats are not sufficient, non-standard floating-point formats matching with the standard ones are constructed, by putting precision variables into floating-point formats and using standard floating-point formats for storing non-standard ones. A fast searching algorithm is designed, making it possible to find out the chaotic periods under different floating-point precisions. Using Visual C++ 6.0, the periods of eleven 1-D chaotic systems, four 2-D chaotic systems and TD-ERCS (Tangent-Delay Ellipse Reflecting Cavity map System) are measured, by condition of different initial iterating values, different system parameters, or different floating-point computing precisions. Factors impacting periods are figured out. Using a linear fitting method, the distribution relationship between periods and numerical precisions is obtained, which corrects the one based on fixed-point formats. Moreover, it gives a rational criterion for the study of chaotic anti-degradation mechanism. This paper also shows that for chaotic systems, conclusions based on fixed-point formats can not be simply extended to ones based on floating-point formats.