基于交替量子随机行走的改进AES和离散余弦变换的图像加密算法

随着科学技术手段飞速发展，图像加密算法被破解的风险也逐渐增加. AES(advanced encryption standard)算法虽然性能优越，但也存在着密钥固定等问题，未来量子计算机的问世将会对此造成重大威胁. 首先，该文采用离散余弦变换(discrete cosine transform, DCT)对明文图像进行DCT域的变换；其次，利用交替量子随机行走构造概率分布矩阵，对概率分布矩阵进行预处理，与DCT后的明文进行逐位异或的操作；最后，计算概率分布矩阵的奇异值，并给出对应的十六进制表达式作为AES的密钥，随机提取概率分布矩阵的一个元素，按照AES算法的编码规则构建轮常量Rcon，进而改进AES算法的加密迭代函数. 测试结果表明，该算法具有很好的加密效果和较高的鲁棒性，密文图像相邻像素在3个方向上的相关系数可以达到0.001 5的显著效果.

An image encryption scheme based on quantum logistic map

With the rapid development of science and technology, the risk of image encryption algorithm being cracked is gradually increasing. Although AES (advanced encryption standard) algorithm has superior performance, it also has the problem of key fixation, which poses a major threat to the advent of quantum computers in the future. First, discrete cosine transform (DCT) was used to transform plaintext images in DCT domain. Second, the probability distribution matrix was constructed by alternating quantum random walk, and the probability distribution matrix was preprocessed to perform bit by bit XOR with the plaintext after DCT. Finally, the singular value of the probability distribution matrix was calculated, and the corresponding hexadecimal expression was given as the AES key. An element of the probability distribution matrix was randomly extracted, and the round constant Rcon was constructed according to the coding rules of the AES algorithm, thereby improving the encryption iteration function of the AES algorithm. The test results show that the algorithm has good encryption effect and high robustness, and the correlation coefficient of adjacent pixels in the ciphertext image in three directions can reach 0.001 5.