基于雅克比椭圆混沌映射的图像加密算法研究

摘要

针对混沌映射会产生瞬态效应，且低维、单峰混沌映射加密算法存在密钥空间小，安全性低等缺点，为此提出一个新的雅克比椭圆混沌映射来加密图像，并将位置集合置乱方法与加密变换函数引入到本文算法中。将明文图像转换成一维矩阵；然后输入初始密钥，迭代雅克比椭圆映射，以消除瞬态效应；由加密变换函数与初值来改变原密钥，根据所得到的新密钥再次迭代雅克比椭圆映射，得到一维阵列；采用位置集合置乱方法处理该阵列，得到一个位置集合，利用该集合置乱图像；采用密钥流机制量化置乱前的阵列，得到一组新阵列，利用新阵列通过加密变换函数对置乱图像中的每个元素进行加密。借助MATLAB仿真平台进行验证，结果表明：改进算法的安全性高，密钥空间大。%Due to the chaotic maps producing the transient effect, and the defects such as small key space and low security existing in current chaotic map encryption algorithm, the Jacobian elliptic map was proposed in this paper to encrypt the image and introduce the permutation method of position set as well as encryption transformation function into the encryption algorithm. The plain-image matrix was transformed into one dimension matrix;and then input the initial key, using the Jacobean elliptic map to iterate to eliminate the transient effect. The encryption transformation function and initial condition were used to modify the initial key, the new key was used to iterate the Jacobean elliptic map one time to obtain the one-dimension array, and the one-dimension array was treated by position set permutation method to permute the initial image. Use the key stream mechanism to treat the one-dimension array to obtain one new sequence for encrypting the elements of permutation-image by encryption transformation function. Finally, the MATLAB simulation platform was used to test this algorithm, and the results show that this algorithm has a higher se-curity.