Abstract
In this paper, we analyzed the periodicity of discrete Logistic and Tent sequences with different computational precision in detail. Further, we found that the process of iterations of the Logistic and Tent mapping is composed of transient and periodic stages. Surprisingly, for the different initial iterative values, we first discovered that all periodic stages have the same periodic limit cycles. This phenomenon has seriously affected the security of chaotic cipher. To solve this problem, we designed a novel discrete chaotic sequence generator based on m-sequence and discrete chaotic mapping. The experimental results indicated that the chaotic sequence generator can generate pseudorandom chaotic sequences with large periodicity and good performance under the condition of limited computational precision.
Highlights
Chaos is a new interdisciplinary theory of physics, mathematics, nonlinear dynamics, and so on
For the digital chaotic sequence generator, performance of the discrete chaotic sequence is seriously affected by the limited computational precision of processor, which will cause the quantized the chaotic binary sequences to have short periodicity and cannot meet the requirements of cryptography [9, 10]
Based on the above experimental results and theoretical analysis, we found that a large number of short-period phenomena occur in discrete chaotic sequences under the influence of limited computational precision
Summary
Chaos is a new interdisciplinary theory of physics, mathematics, nonlinear dynamics, and so on. For the digital chaotic sequence generator, performance of the discrete chaotic sequence is seriously affected by the limited computational precision of processor, which will cause the quantized the chaotic binary sequences to have short periodicity and cannot meet the requirements of cryptography [9, 10] Aiming at this problem, Du et al [11] proposed a novel chaotic key sequence generator based on double K-L (Karhunen-Loeve) transform. Cao et al [18] came up with a Complexity new perturbation method based on Lyapunov exponent to improve random distribution of chaotic sequences These schemes do not consider the effect of chaotic initial value on chaotic sequence and key space.
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