本科毕业论文（设计、创作）
题 目： 混沌数字图像加密技术研究与仿真实现
学生姓名：
学号：
院（系） ： 电子信息工程学院 专业： 通信工程
入学时间：
年
月
导师姓名：
职称/学位： 讲师/硕士
导师所在单位：
完成时间： 年 5 月
I
混沌数字图像加密技术研究与仿真实现
摘 要
近年来，图像数据信息的安全性逐渐受到人们的关注，为了保证图像的可靠传输，混沌系统被引
入图像加密技术。本文主要研究了两种基于混沌系统的图像加密方案。第一种方案是基于超混沌系统
和 DNA 编解码运算相结合的图像加密算法，该算法对图像分块进行加密，由混沌系统生成的混沌序
列决定每一图像块的 DNA 编解码和运算方式。针对该算法密钥空间较低以及不能抵御裁剪攻击的问
题，本文增加了算法中混沌系统的个数，优化了加密的流程。仿真结果表明改进后的加密算法密钥容
量提升至 10
127
数量级，可以抵抗穷举密钥攻击；加密后图像相邻元素相关性降低至 10
-3
数量级，且
加密后图像具备抗裁剪性能。另一方面，基于超混沌系统和 DNA 编解码运算的加密算法复杂度较高，
不适用高效图像加密应用场景，因此本文又研究了基于混沌系统和离散余弦变换（DCT）相结合的图
像加密压缩算法。此类算法可以在保证图像安全性的同时对图像数据进行压缩，从而提升图像传输的
效率。鉴于传统混沌系统 DCT 加密算法的加密过程比较单一，本文在此基础上引入了符号加密，并且
将加密后的结果存储为一维数据。仿真结果表明改进后算法的密钥容量达到 10
74
数量级。当压缩率低
于 64:10 时，解密后还原的图像在视觉效果上和原始图像区别较小，同时，可以根据实际需要，更改
压缩矩阵从而获得不同的压缩率，从而提升图像的传输效率。
关键词：图像加密；混沌系统；DNA 编解码运算；离散余弦变换
II
Research and Simulation of Chaotic Digital Image Encryption
Technology
Abstract
In recent years, the security of image data has been paid more and more attention. In order to ensure the
reliable transmission of images, the chaotic system is introduced into image encryption technology. This
paper mainly studies two image encryption schemes based on chaotic systems. The first scheme is an image
encryption algorithm based on the combination of hyperchaotic system and DNA encoding, decoding and
computing. This algorithm encrypts the blocks of image. The chaotic sequence generated by the chaotic
system determines the DNA coding, decoding, and computing modes of each image blocks. For the problem
that the algorithm has a low key space and cannot resist the cropping attack, this paper increases the number
of chaotic systems in the algorithm and optimizes the encryption process. The simulation results show that
the key capacity of the improved encryption algorithm is improved to 10
127
order of magnitude, which can
resist the exhaustive key attack; after the encryption, the correlation of the adjacent elements of the image is
reduced to 10
-3
orders of magnitude, and the encrypted image has the anti-clipping performance. On the other
hand, encryption algorithms based on hyperchaotic systems and DNA coding, decoding and computing are
highly complex and are not suitable for the application scenarios of high-efficiency image encryption.
Therefore, this paper also studies an image encryption and compression algorithm based on chaotic systems
and discrete cosine transform (DCT). Such algorithms can compress image data while ensuring image
security, thereby improving the efficiency of image transmission. In view of the fact that the encryption
process of the traditional chaotic DCT encryption algorithm is relatively simple, this paper introduces symbol
encryption and stores the encrypted result as one-dimensional data. The simulation results show that the
improved algorithm has a key capacity of 10
74
orders of magnitude. When the compression rate is lower than
64:10, the image after decryption has little difference with the original image on the visual effects. In addition,
the compression matrix can be changed to obtain different compression rates according to actual needs,
which can improve the image transmission efficiency.
Keywords: image encryption; chaotic system; DNA coding-decoding-computing;
discrete cosine transform
III
目 录
1 绪论 ............................................................................................................................................. 1
1.1 课题研究背景和意义 .............................................................................................................. 1
1.2 课题研究现状 .......................................................................................................................... 1
1.3 本文主要研究内容及结构安排 .............................................................................................. 2
2 混沌系统与 DNA 编码 .............................................................................................................. 3
2.1 混沌系统 .................................................................................................................................. 3
2.1.1 混沌的特性 ........................................................................................................................... 3
2.1.2 Logistic 映射 ......................................................................................................................... 3
2.1.3 Chen 超混沌系统 .................................................................................................................. 3
2.2 DNA 编解码与运算 ................................................................................................................. 4
2.2.1 DNA 编码与解码规则 .......................................................................................................... 4
2.2.2 DNA 运算法则 ...................................................................................................................... 5
3 基于混沌系统与 DNA 运算的图像加密系统 .......................................................................... 7
3.1 加密算法思想 .......................................................................................................................... 7
3.2 加密算法具体步骤 .................................................................................................................. 8
3.3 解密算法具体步骤 ................................................................................................................ 10
3.4 实验仿真及性能分析 ............................................................................................................ 11
3.4.1 实验仿真结果 ..................................................................................................................... 11
3.4.2 直方图分析 ......................................................................................................................... 12
3.4.3 相邻位置数据值关联性 ..................................................................................................... 12
3.4.4 抗裁剪性能 ......................................................................................................................... 16
3.4.5 抗噪声性能 ......................................................................................................................... 18
3.4.6 图像质量评价 ..................................................................................................................... 19
3.4.7 信息熵 ................................................................................................................................. 20
3.4.8 密钥敏感性 ......................................................................................................................... 21
3.4.9 密钥容量 ............................................................................................................................. 23
4 基于混沌系统与 DCT 变换的图像压缩加密系统 ................................................................ 24
4.1 加密算法结构 ........................................................................................................................ 24
4.2 DCT 压缩加密算法具体步骤 ............................................................................................... 24
4.3 DCT 解密解压算法步骤 ....................................................................................................... 26
4.4 实验仿真及性能分析 ............................................................................................................ 27
IV
4.4.1 实验仿真结果 ..................................................................................................................... 27
4.4.2 不同压缩比情况下的解密结果 ......................................................................................... 28
4.4.3 密钥敏感性分析 ................................................................................................................. 29
4.4.4 密钥容量计算 ..................................................................................................................... 29
5 总结与展望 ............................................................................................................................... 30
5.1 总结 ........................................................................................................................................ 30
5.2 展望 ........................................................................................................................................ 31
主要参考文献 ............................................................................................................................... 32
致谢 ............................................................................................................................................... 33
