基于改进标准映射的图像加密算法

A Novel Image Encryption Algorithm Based on Improved Standard Mapping

摘要: 本文提出一种基于改进标准映射的图像加密算法。首先，针对标准映射用于图像置乱加密时的密钥空间小等不足，通过引进变量的非线性项和含参量的线性组合对标准映射进行改进。改进标准映射的相位空间图、Lyapunov指数、时间序列测试均表明了改进标准映射具有良好的随机性能。同时，利用改进标准映射设计了一种新的灰度图像加密算法，在置换阶段，采用改进的标准映射实现置乱得到较好的置乱效果；在扩散阶段，采用动态反馈方式的机制使得扩散过程有很好的扩散加密效果。最后，本文还提出了与本文灰度图像加密算法相关的性能分析，包括密钥空间分析、密钥敏感性分析、统计分析等，所有的仿真实验均表明，本文提出的加密算法对各种已知攻击具有非常强的鲁棒性，并且具有密钥空间大、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: This paper proposes an image encryption algorithm based on improved standard mapping. The standard mapping is improved by introducing the nonlinear term of the variables and the linear combination of the parameters. The phase space diagram, Lyapunov exponent and time series tests of the improved standard mapping show that improved standard mapping has good random performance. A new gray image encryption algorithm is then designed using the improved standard mapping. In the permutation stage, the improved standard map is applied to disorder the pixels positions to achieve good scrambling effect. In the diffusion stage, the mechanism of dynamic feedback is used to make the diffusion process have fair diffusion and encryption effect. Finally, the performance analysis is carried out, including key space analysis, key sensitivity analysis, statistical analysis, etc. Simulation experiments show that the encryption algorithm proposed has a large key space, strong key sensitivity, strong robustness against statistical analysis attack, brute force attack, differential analysis attack, and chosen\known plaintext attacks, etc.