基于分数阶超混沌系统的彩色图像压缩加密算法研究

To overcome the simplicity and the security defects of the image encryption algorithms based on chaotic systems of integer order because of keeping pixel positions scrambling as the central step, secure and efficient color image compression-encryption hybrid algorithms will be investigated and proposed by combining fractional hyperchaotic systems with image compression technologies. Specifically, novel color image compression-encryption algorithms based on multi-parameter fractional hyperchaotic systems and neural network, fractional hyperchaotic systems and compressive sensing, nonlinear chaotic systems, and hyperchaotic cat maps will be mainly researched, respectively. To guarantee a more complex relationship among plaintext, cipertext and key of these algorithms, plaintext image will be embedded into the intermediate key sequences and nonlinear iteration operations will be executed on the plaintext image to fulfill encryption. According to common attack methods, the strength and the performance of these proposed image compression and encryption algorithms will be optimized, multiple functions, such as compression and encryption, will be realized simultaneously, and the security and the compression of these hybrid image compression and encryption algorithms will be ensured further. This proposal will enhance the security and usability of image encryption algorithms, enlarge key space, reduce encrypted data volume, and will make breakthrough in performance of color image compression-encryption hybrid algorithms based on fractional hyperchaotic systems. Therefore this proposal is supposed to be of great significance and apparent novelty.

针对基于整数阶混沌系统的图像加密算法因以像素位置置乱为核心而导致算法单一和安全性不高的难题，本项目拟基于分数阶超混沌系统与图像压缩技术深入研究并提出安全高效的彩色图像压缩加密融合算法。本项目具体将重点研究基于多参数的分数阶超混沌系统和神经网络的图像压缩加密算法、基于分数阶超混沌系统与压缩感知的彩色图像压缩加密算法、基于非线性混沌系统的彩色图像压缩加密算法和基于超混沌猫脸变换的图像加密方案。为了保证算法中明文、密文和密钥间的关系更复杂，拟将明文图像信息嵌入中间密钥序列并对明文图像执行非线性迭代运算。针对常见攻击方法，进一步优化新算法的强度和性能，同时实现对彩色图像的压缩和加密等多种功能，确保算法的安全性和压缩性。本项目将完善图像加密算法的安全性和可用性，增大密钥空间，减少加密数据量，并将使基于分数阶超混沌系统的彩色图像压缩加密算法获得性能突破。因而本项目应具有重要研究意义和明显创新性。

针对目前图像加密方案效率不高、难以满足大量图像数据安全需求等不足，本项目基于分数阶超混沌系统与图像压缩等技术深入研究并提出了安全高效的彩色图像压缩加密融合算法。基于无穷平衡点的新四维混沌系统、四维超混沌Henon映射、复合混沌系统、具有自激发吸引子和隐藏吸引子的新四维混沌系统和六维非退化离散超混沌系统等，本项目提出了一系列安全可靠的多幅图像加密方案。本项目深入研究光学域变换与置乱矩阵，结合DNA序列操作和RSA算法、离散余弦变换、四元数离散分数阶哈特莱变换、改进型像素自适应扩散算法、三维正交拉丁方阵与匹配矩阵、受高斯光阑限制的保实分数梅林变换等设计了一系列安全快速的图像加密算法。充分利用量子信息和量子计算的特点和优势，本项目还基于Daubechies D(4)量子小波变换、量子离散余弦变换、猫脸变换、循环移位操作、迭代的量子Fibonacci变换、短记忆分数阶Lotka-Volterra系统、被测交替量子游走和量子逻辑混合线性-非线性耦合映射格等提出了一系列安全有效的量子图像加密算法。此外，结合contourlet变换、奇异值分解鬼成像、多重变换、四电平离散小波变换、优化策略，本项目提出了一系列不可感知的鲁棒数字水印算法。. 项目组按计划圆满完成了相应的研究任务。该项目共发表SCI论文33篇；培养了博士后1人，博士生4人(其中2人获博士学位，2人在读)，硕士生24人(16人获硕士学位，8人在读)，培养青年教师2人。5篇论文获得江西省优秀硕士学位论文。这些研究结果有力支撑了相关学科和重点实验室的建设。本项目丰富了基于超混沌系统的彩色图像压缩加密技术，可为图像压缩加密和数字水印研究提供有益参考。