一种新的分段非线性混沌映射及其性能分析

结合线性反馈移位寄存器（LFSR）和混沌理论各自的优点,采用循环迭代结构,给出一种将LFSR和混沌理论相结合的伪随机序列生成方法.首先根据LFSR的计算结果产生相应的选择函数,通过选择函数确定当前迭代计算使用的混沌系统,应用选择的混沌系统进行迭代计算产生相应的混沌序列；然后把生成的混沌序列进行数制转换,在将得到的二进制序列作为产生的伪随机序列输出的同时将其作为反馈值与LFSR的反馈值进行相应的运算,运算结果作为LFSR的最终反馈值,实现对LFSR生成序列的随机扰动.该方法既可生成二值伪随机序列,也可生成实值伪随机序列.通过实验对生成的伪随机序列进行了分析,结果表明,产生的序列具有良好的随机性和安全性.

A new piecewise nonlinear chaotic map and its performance

Properties of logistic chaotic map is studied, and it is pointed out that phase space is not ergodic when parameters of the chaotic system change. Based on these analysis, a piecewise logistic chaotic map is constructed. The bifurcation diagram and Lyapunov exponent of logistic and piecewise logistic map are studied, and the properties of randomicity, correlation coefficient and power spectrum etc. of the sequences generated by these two maps are analyzed experimentally. A new performance evaluation index for chaotic system, the bifurcation iteration time, is defined. Simulation results show that the defined piecewise logistic map is not only ergodic in phase space, and its corresponding chaotic performance evaluation indices are also better.