In this paper, a novel zig-zag scan-based feedback convolution algorithm for image encryption against differential attacks is proposed. The two measures Number of Pixel Change Rate (NPCR) and Unified Average Changed Intensity (UACI) are commonly utilized for analyzing the differential attacks. From the study of the existing papers, even though high Number of Pixel Change Rate and Unified Average Changed Intensity values are obtained, a few values lie in the critical range of α-level significance which in turn increase the possibility of differential attacks. To overcome differential attacks, two aspects of scanning with different test cases are analyzed and from these analyses, it is concluded that zig-zag scan based feedback convolution in forward and reverse direction achieves good Number of Pixel Change Rate and Unified Average Changed Intensity without critical values. Zig-zag scan based feedback convolution in forward and reverse direction is enforced for key sequence generation and applied in diffusion process to achieve high level of security. Moreover, plain image related initial seed is also generated to overcome the chosen/known plain text attacks. Both numerical and theoretical analyses are performed to prove that the proposed encryption method is resistant to differential attacks. General security measures are carried out for the proposed method to validate its security level. From the simulations, it is shown that the proposed methodology has good keyspace, high key sensitivity, good randomness, and uniform distribution of cipher image pixels.

本文提出了一种基于之字形扫描的反馈卷积算法，用于差分攻击的图像加密。像素变化率（NPCR）和统一平均变化强度（UACI）这两种度量通常用于分析差分攻击。通过对现有论文的研究，即使获得了较高的像素变化率和统一的平均变化强度值，也有一些值处于α的临界范围内级别的重要性，进而增加了差异攻击的可能性。为了克服差分攻击，分析了使用不同测试用例进行扫描的两个方面，并从这些分析中得出结论，基于Zig-zag扫描的正反反馈回旋卷积可实现良好的像素变化率数量和统一的平均变化强度，而不会产生临界价值观。正向和反向基于Zig-zag扫描的反馈卷积被执行以生成密钥序列，并应用于扩散过程中以实现高级别的安全性。此外，还生成了与纯图像有关的初始种子，以克服选择的/已知的纯文本攻击。数值分析和理论分析都证明了所提出的加密方法能够抵抗差分攻击。针对所提出的方法执行了一般安全措施，以验证其安全级别。仿真结果表明，该方法具有良好的密钥空间，较高的密钥敏感性，良好的随机性和密码图像像素的均匀分布。