基于稀疏矩阵的Arnold数字图像加密算法

Arnold digital image encryption algorithm based on sparse matrix

针对原有Arnold数字图像加密算法中常见的密钥空间不足的问题,提出了一种基于稀疏矩阵的Arnold数字图像加密算法——SMA;同时为了进一步提高该基于稀疏矩阵的Arnold数字图像加密算法的安全性,利用图像分层及三层加密结构的思想来加以改进,提出了安全性提升算法——3SMA(3 round SMA)。SMA算法的加密流程首先利用Arnold变换将明文图片扩散到一个较大的稀疏矩阵中,再去除稀疏矩阵中的无效元素得到密文;解密时输入密文图片,依照预先计算好的对换表将密文中的像素调整回原来的位置得到明文。3SMA算法使用三个不同的轮密钥,每一轮都处理明文图像中的两个颜色分量以达到加密的目的。实验表明,与已有的Arnold数字图像加密算法进行对比时,SMA与3SMA算法具有更高的安全性。

For the common key space shortage problem found in existing Arnold digital image encryption algorithm, a new digital image encryption algorithm--SMA （Sparse Matrix Arnold） based on sparse matrix and Arnold transformation was proposed and in order to further improve the security of the algorithm, an improved algorithm--3SMA （3 round SMA） using the ideas of multi-layered decomposition and three-tier structure encryption was proposed. The SMA algorithm adopted Arnold transform to spread the plaintext picture into a large sparse matrix, and then removed invalid sparse matrix elements to get the cipher text. While, the decryption of SMA needed to enter the cipher text picture, and moved pixels in cipher text picture back to their original positions in accordance with the previously computed swapping table. The 3SMA algorithm comprised three different round keys. Each round, the improved algorithm needed to process two color components of the plaintext picture to achieve the purpose of encryption. The experimental results show that the proposed encryption algorithm and its improvement obtain higher security compared to Arnold encryption algorithms analyzed.