新二维离散超混沌映射及其在图像加密的应用

A New Two-dimensional Discrete Hyperchaos Mapping and Its Application in Image Encryption

在分析logistic映射和cubic映射的基础上,针对一维映射混沌区间窄、映射函数简单的综合考量,提出了一种新的超混沌二维离散映射.该映射系统参数混沌区间大于logistic映射和cubic映射,映射值域也同样大于前二者,同时存在2个正的Laypunov指数的超混沌现象.迭代运算受计算机精度影响方面也低于一维映射.对其产生的二值伪随机序列进行了NIST标准测试,其随机性明显好于logistic和cubic映射.最后提出一个基于该二维映射的图像灰度加密算法,相比logistic和henon加密增大了密钥空间、降低了映射迭代的时间复杂度.

Based on logistic mapping and cubic mapping, for one dimensional mapping chaotic narrow range and simple of mapping function, this paper proposes a new two-dimensional discrete hyperchaos mapping. The chaotic interval of system＇s parameters is greater than the logistic mapping and cubic mapping, mapping domain is also greater than before, and there are two positive Laypunov indexs with having a hyperchaos phe- nomenon that. Iterative operation affected by the precision of computer is less than one dimensional mapping. The binary pseudorandom sequence of mapping is tested by NIST, resulting shows that the randomness of two-dimensional mapping is much better than logistic mapping and cubic mapping. Finally, putting forward a grayscale image encryption algorithm based on the two-dimensional mapping. The algorithm is compared with the logistic and Henon encryption increases the key space, reduces the time complexity of mapping iterative.