Abstract: Traditional image encryption algorithms have some shortcomings such as weak theory about key generating, fixed-length key, limited key-value range. Aiming at these disadvantages, a variable-length running key image encryption algorithm with solid theory foundation is proposed. At first, uniform trend theorem and the deviation theorem are given, then according to these theorems, uniform generation algorithm of chaotic sequence is designed, which is used to generate uniform distribution random number. On this basis, this random number is used to generate the length of plain-text and corresponding length key. At last, variable-length key image encryption scheme with one-time key stream is implemented by using cipher-text disturbance chaotic sequence and random feedback encryption technique. Theory analysis and experimental results show that the proposed image encryption algorithm not only inherits the merit of one-time key of traditional encryption scheme, but also increases the difficulty of crack and enhances the security of image encryption algorithm since solid theory, variable-length encryption mechanism and key space and its value flexibility.

Key words: chaos, image encryption, variable-length key, one-time key stream

摘要： 针对传统图像加密算法，密钥生成理论不坚实，密钥长度固定，取值范围有限的不足，提出具有坚实理论基础的变长密钥图像加密算法。给出均匀化趋势定理和偏差定理，然后依据该定理设计了混沌序列均匀化生成算法，用于生成服从均匀分布的随机数。在此基础上，应用该随机数生成欲加密明文长度以及对应长度的密钥，并通过密文随机扰动混沌序列和随机反馈加密技术，实现了具有一次密钥流的变长密钥图像加密。理论分析和实验结果表明，提出的图像加密算法不仅继承了传统加密算法的一次密钥流的优点，而且由于理论坚实且引入变长密钥加密机制，密钥空间及其取值具有伸缩性，增加了破译难度，增强了图像的安全性。

关键词: 混沌, 图像加密, 变长密钥, 一次密钥流