摘要
本文提出了一种基于新的五维多环多翼超混沌系统的数字图像加密方法.首先,将明文图像矩阵和五条混沌序列分别通过QR分解法分解成一个正交矩阵和一个上三角矩阵,将混沌系统产生的五条混沌序列分别通过LU分解法分解成一个上三角矩阵和一个下三角矩阵,分别将两个上三角矩阵和一个下三角矩阵相加,得到五个离散后的混沌序列;其次,将明文图像矩阵分解出来的正交矩阵与五个混沌序列分解出来的五个正交矩阵相乘,同时把明文图像矩阵分解出来的上三角矩阵中的元素通过混沌序列进行位置乱,再将操作后的两个矩阵相乘;最后,将相乘后的矩阵通过混沌序列进行比特位位置乱,再用混沌序列与其进行按位“异或”运算,得到最终加密图像.理论分析和仿真实验结果表明该算法的密钥空间远大于10^200,密钥敏感性强,能够有效地抵御统计分析和灰度值分析的攻击,对数字图像的加密具有很好的加密效果.
The complex structure of hyperchaos and its complex dynamic behavior have a good application prospect in the fields of image encryption,digital watermarking and information security.Therefore,it has become very important to generate chaotic attractors with multi-vortex and multi-winged multi-rings with complex topologies.In this paper,we propose a new five-dimensional hyperchaotic system capable of generating multiring and multi-wing,and carry out theoretical analysis and numerical simulation experiments on some basic dynamic characteristics of the chaotic system.Such as equilibrium point,dissipation,Lyapunov exponent,bifurcation diagram,phase diagram and so on.In the process of encryption,first,we decompose the plaintext image matrix and the five chaotic sequences into an orthogonal matrix and an upper triangular matrix by QR decomposition.The five chaotic sequences generated by the chaotic system are respectively decomposed into an upper triangular matrix and a lower triangular matrix by the LU decomposition method.The upper triangular matrix decomposed by the QR decomposition method and the lower triangular matrix decomposed by the LU decomposition method are respectively added to obtain five discrete chaotic sequences.At the same time,the five discrete chaotic sequences are added to the upper triangular matrix decomposed by the LU decomposition method to obtain the final five discrete chaotic sequences.Secondly,the orthogonal matrix decomposed by the plaintext image matrix is multiplied by five orthogonal matrices decomposed by five chaotic sequences.At the same time,the elements in the upper triangular matrix decomposed by the plaintext image matrix are chaotically arranged by the chaotic sequence,and then the two matrices after the operation are multiplied.Finally,the multiplied matrix is chaotically placed on the bit by a chaotic sequence.Then use the chaotic sequence to perform a bitwise XOR operation to obtain the final encrypted image.The theoretical analysis and simulation results show that the algorithm has large key space and strong key sensitivity.It can effectively resist the attacks of statistical analysis and gray value analysis,and has good encryption effect on digital image encryption.This image encryption algorithm using a combination of conventional encryption and chaotic encryption does not have a defined plaintext ciphertext mapping relationship.
作者
庄志本
李军
刘静漪
陈世强
Zhuang Zhi-Ben;Li Jun;Liu Jing-Yi;Chen Shi-Qiang(School of Science,Hubei Mimzu University,Enshi 445000,China;School of Information Engineering,Hubei Minzu University,Enshi 445000,China;School of Advanced Materials and Mechatronic Engineering,Hubei Minzu University,Enshi 445000,China)
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2020年第4期18-31,共14页
Acta Physica Sinica
基金
湖北民族学院博士启动基金(批准号:MY2018B014)
国家自然科学基金(批准号:61562025)资助的课题~~
关键词
五维超混沌系统
正交分解
比特位扰乱
数字图像加密
five-dimensional hyperchaotic system
orthogonal decomposition
bit disturb
digital image encryption
