In recent years, image encryption has become a very popular and effective method to protect digital images. Among many image encryption methods, the image encryption algorithm based on chaotic map has extensive application and profound theoretical basis. In this paper, a novel image encryption algorithm is proposed by combining chaotic map with Josephus problem. The whole encryption process adopts the classical permutation–diffusion structure. In the permutation process, the double chaotic cycle shift algorithm has been proposed by improving the chaotic shift transform method. In the diffusion stage, we extend the definition of Josephus problem by using chaotic map to preserve the Josephus sequence diversity. We then divide the image into sub-blocks and pick one randomly according to Josephus sequence. Furthermore, we change the pixel values of the image through performing modular addition and XOR operations on the pixels between blocks. Through the above process, we get the image encryption algorithm based on double chaotic cycle shift and Josephus problem (JP-DCCS). In the simulation experiment and security analysis, we compare JP-DCCS with the other advanced image encryption algorithms. The results show that JP-DCCS has better performance and higher security.

近年来，图像加密已成为保护数字图像的一种非常流行和有效的方法。在众多的图像加密方法中，基于混沌映射的图像加密算法具有广泛的应用和深刻的理论基础。本文提出了一种将混沌映射与约瑟夫斯问题相结合的新型图像加密算法。整个加密过程采用经典的置换扩散结构。在置换过程中，通过改进混沌移位变换方法，提出了双混沌循环移位算法。在扩散阶段，通过使用混沌图谱来保留约瑟夫斯序列的多样性，扩展了约瑟夫斯问题的定义。然后，我们将图像划分为子块，并根据约瑟夫斯序列随机选择一个。此外，我们通过对块之间的像素执行模块化加法和XOR操作来更改图像的像素值。通过以上过程，我们得到了基于双混沌循环移位和约瑟夫斯问题的图像加密算法（JP-DCCS）。在仿真实验和安全性分析中，我们将JP-DCCS与其他高级图像加密算法进行了比较。结果表明，JP-DCCS具有更好的性能和更高的安全性。