基于混沌Gyrator变换与矩阵分解的光学图像加密算法

Color image encryption algorithm based on chaotic gyrator transform and Matrix decomposition

为了解决当前光学图像加密技术没有考虑明文自身特性,使其抗明文攻击能力较低,且易增加密钥的分配与管理难度的问题,设计了基于混沌Gyrator变换与矩阵分解的非对称彩色图像加密算法。首先,从彩色图像中分别获取其R、G、B分量;设计二维耦合混沌系统,生成3个随机相位掩码,分别对R、G、B分量进行调制;基于卷积操作,将调制后的R、G、B分量融合为一幅灰度图像;利用混沌系统输出的随机序列来计算Gyrator机制的旋转角度,对灰度图像完成Gyrator变换,获取Gyrator频谱;根据相位-幅度截断机制,对Gyrator图像完成截断操作,形成幅度与相位信息;再引入一种矩阵分解机制,将相位截断图像分解为酉矩阵与三角矩阵,利用旋转角度不同的Gyrator变换分别处理酉矩阵与三角矩阵,完成图像加密。在图像加密过程中,利用其幅度截断图像信息来生成R、G、B分量的解密密钥,使得加密与解密密钥是截然不同的,只需利用私钥即可解密图像。测试数据表明,与较为主流的光学加密方案相比,所提技术具备更高的安全性,可有效抗击明文攻击。

In order to enhance the ability to resist plain attack and better the management in current optical image encryption technology.An asymmetric color image encryption algorithm based on chaotic Gyrator transform and matrix decomposition was designed in this paper.Firstly,the R,G and B components were obtained from the color image.A two-dimensional coupled chaotic system was designed to generate three random phase masks for modulating R,G and B components respectively.And the modulated R,G and B components were fused into a grayscale image.Then the rotation angle of the Gyrator mechanism was calculated by the random sequence,and the Gyrator transform was used to process the grayscale image for obtaining the Gyrator spectrum.The Gyrator spectrum was processed based on the phase-amplitude truncation mechanism to output two coded images.Finally,the phase truncated image was decomposed into a unitary matrix and a triangular matrix based on matrix decomposition mechanism,and image encryption was completed by using the Gyrator transform of different rotation angles to process the unitary matrix and triangulation matrix.In the process of image encryption,the decryption key of R,G and B components were generated by using its amplitude-truncate image information which make its encryption and decryption key completely different,and the image can be decrypted by only using the private key.The experimental results show that the proposed algorithm has higher security level compared with the current optical image encryption technology.