摘要
随着信息技术的发展和多媒体应用的快速增长,多媒体信息如语音、图像、视频等已经成为了现代生活中不可或缺的一部分。人们通过电脑和互联网浏览图像和视频,利用医学图像进行疾病诊断,军事图像提供决策,进行商业视频会议等然而,随着多媒体应用的不断深入和攻击方式的不断发展,多媒体信息特别是图像数据的安全已成为数学、信息技术以及图像处理领域的重要问题。安全可靠的信息安全技术的需求也变得越来越迫切。然而,由于图像数据的一些内在特性如海量数据、高冗余性、高相关性等,使得传统加密方案不再适合图像加密。混乱是确定性的非线性系统内的复杂的、不可预测的看似随机的行为。由于其对初始值和控制参数的敏感性已成为图像加密的一个重要的选择。本文主要利用混沌,超混沌和复合混沌理论并结合数论知识设计了几类图像加密算法,并探讨了图像加密中随机数的产生问题,主要内容如下：
(1)在分析Chebyshev混沌映射和二次剩余密码体制的基础上,提出了一种二次扩散的图像加密算法,将传统加密结构中相互独立的置乱和扩散改为两个连续进行的扩散过程,在扫描一次明文图像的同时,两次扩散操作连续完成。实验分析表明该算法具有较高的安全性和实用性。
(2)分析了二维超混沌离散动力系统的优良混沌特性,利用二维超混沌系统建立了一种经典的FRIDRICH置乱-扩散图像加密算法。在该算法中,利用二维超混沌离散动力系统对图像像素点的位置连续进行二次置乱,然后将置乱后的图像用中国剩余定理改变其像素值,从而达到改变图像信息分布的目的。并验证了算法的有效性。
(3)研究了复合离散混沌系统对初始值和控制参数的敏感性,并设计了一类新的二维复合离散混沌系统。利用二维Logistic映射和二维复合离散混沌系统给出了一种比特层次的图像置乱-扩散算法。与传统的像素层次图像加密算法相比,比特层次的图像置乱-扩散加密方案中,像素值之间的信息是会发生交换的,故置乱和扩散的效果更明显,进一步加强了算法的安全性。
(4)提出了基于Arnold映射和仿射密码的比特-像素层次相结合的图像加密算法。在置乱阶段,利用广义Arnold映射按照随机搜索的方式从明文图像的行方向和列方向分别对明文图像进行两次比特层次的置乱。在扩散阶段,使用仿射密码对图像进行像素层次的图像扩散,增强了FRIDRICH置乱-扩散图像加密体制的安全性和有效性。
(5)探讨了图像加密技术中的随机数的产生问题。提取人体生物特征独特的随机性,同时将生物特征在认证和识别中的噪声利用起来,把密码和生物特征以一种新颖的方式结合起来,设计了一类密码安全的基于虹膜特征的随机数发生器。仿真结果表明了该随机发生器的既具有了伪随机数发生器的产生速度快的优点,同时也具有真随机数发生器优良的随机性的特点。
With the rapid development of information technology and multimedia applica-tion, multimedia information such as sound, image, video, etc has become an indis-pensable part of modern life. The security of multimedia information has become animportant issue in the field of mathematics, communications, information technologyand image processing. How to design a secure and reliable information security tech-nology becomes more and more urgent. Due to some intrinsic features of images suchas bulk data capacity, high redundancy and high correlation, so, traditional encryptionschemes (DES, RSA, IDEA, AES, etc.) is not suitable for image encryption. Chaos isa complicated, unpredictable and seemingly random behavior in a deterministic nonlin-ear system. It has become a vital choice for image encryption because of its sensitivityof initial value and control parameter. In this paper, we design several kinds of imageencryption algorithm with the help of chaos, hyper-chaos, composite chaotic systemtheory and number theory knowledge. The main content of the paper are summarizedbelow:
(1) Considering the traditional image encryption structure, permutation and diffu-sion are two independent procedure, we design an image encryption algorithm with twoconsecutive diffusion process by Chebyshev chaotic map and quadratic residue cipher.Every pixel is diffused twice by scanning the plain image only once, the experimentalanalysis shows the efficiency and security of the algorithm.
(2) We analyze the good chaotic property of2d hyper-chaos discrete dynamic sys-tem, and we establish a classic Fridrich permutation-diffusion image encryption algo-rithm, and utilize2d Hyper-chaos discrete nonlinear dynamical system to scramble theimage pixel position twice, then the Chinese remainder theorem is used to change theimage information distribution by changing the pixel value.
(3) We study the sensitivity to initial value and control parameter of composite dis-cretechaoticsystems, andprovideanew2dcompositediscretechaoticsystem. Consid-eringtheredonotexistinformationexchangebetweendifferentpixelsinpixel-levelim-ageencryptionalgorithm,abit-levelimageencryptionalgorithmusingtwo-dimensional2-d Logistic map and compound chaotic system are presented. Compared with the tra-ditional pixel-level image encryption algorithm, the information of different pixels isexchanged in this bit-level permutation and diffusion procedure. It can strengthen thesecurity of the pixel-level algorithm.
(4)Weproposeanimageencryptionalgorithmwithabit-levelpermutationbygen-eralized Arnold map and pixel-level diffusion by affine cipher. In permutation phase,we scramble the plain image according to a random search way by generalized Arnoldmap in row direction and column direction, respectively. In the diffusion stage, we em-ploy affine cipher to do the pixel-level image diffusion. The simulation results show theproposed algorithm effectively enhances the Fridrich image encryption architecture.
(5) We study the importance of the random number generation problem in imageencryption technology and cryptography field. A novel kind of iris and chaotic-basedrandom number generator (ICRNG) is developed from the unique randomness and ex-ternal noise(which is very tricky in biometrics authentication and identification)in the.This method combines biometric feature extraction and random number generation ina novel way. Experiments demonstrate that ICRNG not only has good performance ingeneration speed, but also has a good randomness performance, which means ICRNGcombines the advantages of pseudorandom number generator and true random numbergenerator.
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