一种Logistic-Fibonacci级联的混沌映射及其性能分析

A Logistic-Fibonacci Cascaded Chaotic Map and Its Performance Analysis

提出一种Logistic与广义三阶Fibonacci级联的混沌映射,用Logistic生成的随机序列作为广义三阶Fibonacci的参数A、B、C,每次迭代参数A、B、C值均得到替换。该方法扩大了混沌控制参数范围,将满映射范围增大至整个控制参数区间,可产生均匀序列解决"稳定窗"与"空白区"等问题。通过与传统Logistic和其他改进Logistic混沌映射进行实验对比,表明Logistic-Fibonacci级联混沌映射在序列分布均匀性、随机性,复杂度、初值敏感性等方面均为最优,可在混沌加密应用中增加密钥个数、增大密钥空间。

A cascaded chaotic map of Logistic and generalized third-order Fibonacci is proposed.The random sequences generated by Logistic are used as the parameters A,B and C of the generalized third-order Fibonacci.The A,B and C are replaced in each iteration.This method expands the parameters range of chaotic.And the full mapping range is extended to the entire control parameter interval.A uniform sequence can be produced by the cascaded chaotic map to solve the problems of"stable window"and"blank zone".Compared with the traditional Logistic and other improved Logistic chaotic map,the experiments results show that the sequence generated by the logistic-Fibonacci cascade chaotic map is optimal in distribution uniformity,randomness,complexity,initial value sensitivity and other aspects.Moreover,the number of keys can be increased to increase the key space in chaotic encryption.