基于离散傅里叶变换融合双混沌映射的图像加密算法研究

摘要

Frequency domain encryption very fits most of digital and optical image processing systems,while spatial domain encryption is applicable for image communications.In order to make full use of image encryption advantages in both frequency domain and spatial domain and further improve the security of image encryption system,we propose an image encryption algorithm which is based on discrete Fourier transformation and doubling chaotic map to encrypt frequency and spatial domains of image simultaneously.Firstly,the two-dimensional discrete Fourier transformation is committed to convert the image from the spatial domain to frequency domain,and the improved subsection Tent map is used to scramble the amplitude and phase of the frequency domain respectively;Secondly,the frequency domain of scrambled image is transformed into spatial domain with Fourier inverse transformation to get scrambling encryption image;Finally,the improved Bernoulli displacement map is applied to the scrambling encryption image for diffusion processing.The proposed algorithm is tested on MATLAB simulation platform,simulation experimental results show that the algorithm is highly secure with large key space and has stronger key sensitivity performance,which effectively improves the ability of resisting the chosen plaintext attack.%频域加密非常适用于大多数数字和光学图像处理体系，而空间域加密则适用于图像通信。为了充分利用在图像频率域和空间域加密的优势，进一步提高图像加密系统的安全性，提出基于离散的傅里叶变换和双混沌映射的图像加密算法，同时对图像的频率域和空间域进行加密。首先，利用二维离散的傅里叶变换将图像从空间域转换成频率域，并用改进的分段Tent映射分别对幅值和位相进行置乱处理；其次，将置乱后图像频率域进行傅里叶逆变换，转换成空间域，获得置乱加密图像；最后，利用改进的Ber-noulli移位映射对置乱加密图像进行扩散处理。在MATLAB仿真平台上，实验结果表明：该算法高度安全，密钥空间大，有较强的密钥敏感性能，有效地提高了抵御选择明文攻击的能力。