基于一维混沌映射和类标准映射的彩色图像加密新算法

A New Color Image Encryption Algorithm Based on One-Dimensional Chaotic Mapping and Quasi-Standard Mapping

摘要: 提出基于一维混沌映射和类标准映射的彩色图像加密新算法。通过改进的一维混沌映射构造出一种新的类标准映射；通过空间相位图、Lyapunov指数曲线和时间序列测试等对其进行了混沌特性分析，分析结果表明新类标准映射具有混沌参数空间大、良好的随机性等混沌特性。基于一维混沌映射和新类标准映射设计了一种彩色图像加密算法。不同于传统的置乱–扩散机制，该算法采用预先扩散–置乱–扩散结构，在预先扩散阶段采用一维混沌映射产生初始向量对明文图像进行预处理，然后利用本文构造的类标准映射产生随机数对预处理后的图像进行加密。本文算法采用一维混沌系统和多维混沌系统对图像按照依行依列的方式对明文图像进行加密，不但安全性大大提高，而且加快了加密的速度。事实上，本文提出算法的安全性能分析包括密钥空间分析、密钥敏感性分析和统计分析等均表明本文提出的加密算法具有密钥空间大、密钥敏感性强、可抵抗统计分析攻击、蛮力攻击、差分攻击、已知明文和选择明文攻击等优良特性。

Abstract: In this paper, a new color image encryption algorithm based on one-dimensional chaotic mapping and quasi-standard mapping is proposed. A new quasi-standard mapping is constructed by an improved one-dimensional chaotic map. The chaotic characteristics of the new quasi-standard mapping are analyzed by spatial phase diagram, Lyapunov exponential curve and time series test. The results show that the new quasi-standard mapping has large chaotic parameter space, good randomness and other chaotic characteristics. Then, a color image encryption algorithm is designed based on one-dimensional mapping and new quasi-standard mapping. It is different from the traditional scrambling-diffusion mechanism. The algorithm uses a pre-diffusion-scrambling-diffusion structure, which uses one-dimensional chaotic mapping creating the initial vector to preprocess the plain image in the pre-diffusion stage, and then the pre-processed image is encrypted by generating the random number and using the new quasi-standard mapping. Furthermore, we encrypt the plain image in row by row and column by column, as a result, the security is greatly improved as well as the speed of encryption is accelerated. In fact, the security performance analysis of the proposed algorithm, including key space analysis, key sensitivity analysis and statistical analysis etc., which shows that the encryption algorithm proposed has large key space, strong key sensitivity and can resist various known attacks, such as statistical analysis attack, brute-force attack, differential attack, known plaintext and chosen plaintext attack, etc.