Abstract: As an important field in information security, image encryption algorithm has been a research focus. A novel image encryption algorithm combining with features of the classic fractal Julia sets is proposed. This algorithm utilizes Julia set to generate the random key and modulo operation method is used for image encryption, and then diffusion process is used twice to generate the encrypted image. Since Julia sets can be generated with only a few parameters, it can reduce the storage space greatly. In addition, Julia sets have infinite structures and chaotic properties. Even the slight disturbance of the parameters can change the key dramatically, which will lead to the wrong decryption of the image. The experimental results show that the algorithm has lager key space and more sensitivity for the key compared to the algorithm proposed by Rozouvan utilizing the Mandelbrot sets as the key. In particular, it can resist chosen-plaintext attack more efficiently.

Key words: Julia sets, modulo operation, diffusion, image encryption

摘要： 作为信息安全的重要领域，图像加密算法一直是人们研究的热点。针对经典分形集合Julia集的特点，提出一种图像加密算法。将Julia集作为一种随机元素生成密钥，采用模运算方法对图像进行加密，对生成的密文进行两次扩散，得到最终密文。由于Julia集密钥仅需几个参数就可以表示，大大减小了存储空间。并且Julia集的无限性以及混沌特性使得任意参数的极其微小的变动都将导致密钥剧烈变化，无法正常解密。该算法较Rozouvan提出的以Mandelbrot分形集为密钥的转换方法，密钥空间更大，密钥敏感性显著提高，尤其能够有效抵御选择明文攻击。

关键词: Julia集, 模运算, 扩散, 图像加密