三维可逆混沌映射图像加密方法及其优化算法

利用混沌拉伸和折叠的原理，提出了一种三维可逆混沌映射图像加密方法及其优化算法。将灰度图像用一个三维数据矩阵描述，根据提出的算法将该三维数据矩阵映射为二维数据矩阵。对此二维数据矩阵应用拉伸和折叠算法实现图像像素的置乱处理。最后将置乱后的二维数据矩阵还原为三维数据矩阵，得到加密图像。该加密方法是可逆的，可用于图像加密和解密。推导了加密和解密算法完整的数学表达式。由于图像数据量大，利用推导的数学表达式实现图像加密和解密时计算量较大，加密时间长，针对这个问题提出了一种优化算法。仿真结果表明该加密方法同时实现了像素置乱和像素混淆，抵御统计攻击的能力增强，密钥敏感度高，优化算法明显提高了加密速度。

Invertible chaotic three-dimensional map based Image encryption approach and its optimized algorithm

An invertible chaotic 3D map based image ecnryption approach and its optimized algorithm are proposed utilizing the stretch and fold mechanism of chaos. A gray-level image is firstly depicted as a 3D matrix. Then the 3D matrix is mapped to a 2D image matrix according to the proposed algorithm. Stretch and fold maps are used to permute pixel positions of the 2D matrix. The stretch process is to transform the 2D image matrix to an array, while the fold process is to fold the array to another 2D image matrix which is the same size as the original 2D matrix. At last, the permuted 2D matrix is mapped back to a 3D matrix, cipher image is achieved. This proposed approach is invertible, it could be used for image encryption and decryption. The encryption and decryption algorithms are formulated. Since image has large data quality, if the deduced formulas are used for image encryption and decryption, there will be large amount of calculation and long encryption and decryption time. In order to solve this problem, an optimized algorithm is proposed. Image encryption and decryption experiments were did and key sensitivity,correlation coefficients of two adjacent pixels and the time used for image encryption and decryption are tested. The results show that proposed image encryption approach realize pixel permutation and substitution at the same time via one iteration map, it change the histogram information of the plain image, enhance the capability of resisting statistic attack, have big key space. The proposed optimized algorithm obviously increase image encryption speed, it is faster than using the deduced formulas about 3 to 4 times.