非线性欠定混合的图像加密

盲源分离技术应用于图像加密其主要原理是利用欠定混合形成的病态问题无法求解来实现加密；但由于盲源分离技术存在着解的顺序和尺度不确定性，并且要求源图像、密钥图像各图像之间尽量没有相关性，这些问题影响了图像解密的效果，也使加密系统适用范围受限；另外已被证实未加预加密处理的欠定混合，其本身抗攻击性较弱。为此，提出了一种基于前置非线性欠定混合的图像加密解密新方法。该方法先利用可逆非线性函数对图像进行处理，再进行欠定混合，获得加密信号；而解密端利用密钥得到等效混合矩阵的逆矩阵，以及非线性函数的逆函数，通过矩阵求逆以及非线性函数的逆运算处理获得与明文图像相同的解密图像。仿真实验和性能分析结果表明，该方法解密质量很好，速度较快，解密图像不存在顺序和灰度值的变化，同时省去图像之间的相关性要求，抗攻击性强。

Nonlinear-Underdetermined Mixture Applied to Image Cryptosystems

Blind source separation technique has been used in image encryption, and the encryption is based on the unsolved ill-posed problem brought by underdetermined mixture. Due to the uncertainty of the order and the scale of the BSS Solution, and the requirement of the uncorrelation between the original images and key images, the effect of the image decryption is affected, and the scope is limited.Moreove, the cryptosystem has been confirmed to be weak against attacks for underdetermined-mixture without pre-encryption process. Therefore, This paper propose a novel method based on preposing nonlinear-underdetermined mixture for image encryption and decryption. This method firstly adopts reversible nonlinear functions to process the images, and then execute underdetermined mixture between these images to get the ciphertext signals. The decryption end could obtain the inversed matrix of the equivalent mixed-matrix and the inverse functions of the nonlinear invertible functions through the keys. then we can get the decrypted images by means of the inverse matrix and inverse functions. Simulation and performance analysis demonstrate thatteh proposed method can provide much higher quality and much faster speed compared to the BSS decyrption and correlation calculation,simultaneously,the decrypted images don't exist the problem of changes from the order and gray value,moveover,the method eliminates the requirement for uncorrelation between the original images and the key images, and have strong resistance to attacks.