改进混沌方程及压缩感知理论图像加密算法

针对传统Logistic混沌系统混沌性能低，生成伪随机序列随机性较差等问题，本文提出一种新的改进Logistic混沌方程，并与Lorenz超混沌系统、压缩感知理论相结合构建一个多混沌图像压缩加密系统。在加密过程中与传统加密算法相结合，进行置乱、扩散操作最终获得密文图像。通过改进的Logistic混沌方程获得随机性能更好的伪随机序列来构造受控测量矩阵，仿真实验表明通过改进的Logistic混沌方程来构造的受控测量矩阵在压缩率为75%的条件下峰值信噪比达到34.26 dB，与传统Logistic混沌方程相比在同等条件下提高约10 dB，并且该算法有较好的抗差分攻击性能，像素改变率（NPCR）与统一平均变化程度（UACI）接近理论值。故本文提出的加密算法具有较好的压缩性、安全性以及信号重建特性。

Improved Image Encryption Algorithm Based on Chaotic Equationand Compressed Sensing Theory

In view of the low chaos performance of the traditional Logistic chaotic system and the poor randomness of generated pseudo-random sequences, in this paper, a new improved Logistic chaotic equation is proposed, and a multi-chaotic image compression and encryption system is constructed by combining Lorenz hyperchaotic system and compressed sensing theory. In the process of encryption, the encryption algorithm is combined with the traditional encryption algorithm to obtain the ciphertext image by scrambling and spreading. The controlled measurement matrix is constructed by using the improved Logistic chaotic equation to obtain a pseudo-random sequence with better random performance. Simulation experiments show that the PSNR of the controlled measurement matrix constructed by the improved Logistic chaotic equation reaches 34.26 dB under the condition of 75% compression ratio, which is about 10 dB higher than that of the traditional Logistic chaotic equation under the same conditions. And the algorithm has a good anti-differential attack performance, pixel change rate (NPCR) and uniform mean change degree (UACI) are close to the theoretical value. Therefore, the encryption algorithm proposed in this paper has good compressibility, security and signal reconstruction characteristics.