Based on the fundamental principle of differential cryptanalysis and corresponding relation between the iteration of chaotic system and the round of block cipher, two important concepts, namely the iterative differential distribution (IDD) and the differential-invalid exponent (DIE) are proposed, which are used in evaluating chaotic system's power of conteracting the differential cryptanalysis. IDD is defined as the distribution of output differential vs. a given input differential at a varied iterative number, and DIE is defined as the minimal iterative number at which both output differential and input differential are independent of each other. By putting chaotic system into the “naked” state and directly analyzing the IDD, the DIE of chaotic system can be gotten. DIE is a universal, measurable and important characteristic exponent of chaos in studying security of chaos. The tests on both TD-ERCS and Logistic systems indicate that in the parameter region of 90%, DIE of DT-ERCS is equal to 2, which is the minimal DIE in theory.In comparison, DIE of Logistic chaotic system equals 55, hence TD-ERCS is a chaotic system with the power of active immunity to differential cryptanalysis.
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