基于三维Arnold变换的数字图像置乱技术及其周期性

以图像信息安全问题为背景，讨论了三维Arnold变换及其逆变换的周期性，并用实例说明三维Arnold变换在数字图像置乱中的作用。     

Hamiltonian Systems: Stable or Unstable?

This is a review concerning some topics in the field of Hamiltonian dynamics, with emphasis on the problem of Arnold diffusion. Lecture held in the Seminario Matematico e Fisico on January 16, 2006 Received: May 2006     

基于混沌与快速小波变换的多光谱图像压缩加密算法

针对多光谱图像存储和传输安全性问题,提出一种将混沌思想、小波变换和KL(karhunen-loeve)变换相结合的多光谱图像压缩加密算法。首先,采用K-means聚类方案将多光谱图像聚类为通用像素,通过选择合适的K值使算法的性能最优,同时便于后续处理;然后对通用像素进行二维离散9/7小波变换,对变换后的系数进行Arnold变换以及加密处理,消除多光谱图像大部分空间冗余,减少压缩过程中的块效应;之后对产生的小波系数进行改进的KL变换,消除残余空间冗余和光谱冗余;最后采用差分脉冲滤波器对系数进行编码,并采用Tent映射对码流进行混淆扩散加密。通过实验可知,本算法的信息熵达到11.794 3(选取12位多光谱图像),信息熵更接近最大值12,优于现有算法,可以更好的隐藏原图特征;该算法的像素变化率(NPCR)和归一化平均变化强度(UACI)分别为99.81%和34.19,优于现有的其他算法,本算法可以更好的抵御差分攻击;输出比特流变化率保持在47.62%～47.71%之间,密文比特流变化率保持在47.45%～47.52%,本算法具有较好的密钥敏感性;在压缩比为4∶1～32∶1范围内,系统PSN...     

一种高效的彩色图像加密和解密算法

分析了基于Amold变换的加密方案在加密效果及加密效率方面的不足。提出了一种新的彩色图像加密及解密算法。加密过程将像素的物理位置置乱并映射到不同的色彩空间;解密过程提出了一种针对彩色图像的逆变换算法,使解密的时间仅依赖加密的密钥而不依赖变换周期。仿真分析比较了该算法在加密效果及加密效率方面的优势。实验数据表明,该加密算法的加密效果理想,且加密效率较高,是一种简单、可行的彩色图像加密方法。     

基于Logistic映射和Arnold置乱的数字水印算法

提出了一种基于Logistic映射和Arnold变换的DCT域数字水印算法。利用Arnold变换将原始水印图像进行置乱,然后对图像进行分块DCT变换,结合Logistic映射控制水印信息的嵌入位置,把置乱后的水印图像嵌入到图像的DCT域中频系数中,进行分块DCT反变换得到水印图像。利用图像DCT系数的关系,实现了水印的盲检测。实验结果表明该算法不仅具有较好的隐蔽性,同时对常见的水印攻击具有较好的鲁棒性。     

一种基于DWT-DCT-SVD的鲁棒性音频水印算法

针对在基于DWT-DCT进行数字音频水印嵌入,在已嵌入水印的音频受到噪声干扰、低通滤波、重采样等常见的攻击时,其鲁棒性差以及安全性弱的情况.提出了一种新的的盲水印嵌入算法.该算法对原始音频信号完成分帧预处理后,对每帧信号应用离散小波变换(DWT),选取三级低频分量进行离散余弦变换(DCT),先把得到的一维信号平均分解为两个片段,然后进行奇异值分解(SVD),根据奇异值的特性将水印信息嵌入到奇异矩阵.在水印图像的预处理上,采用了以Arnold变换为基础,将水印图像降维,方便水印信息的嵌入.并且通过添加密匙来提升数字音频水印的安全性.使用5个不同种类的音乐类型,进行仿真实验.实验结果表明:其误码率(BER)在0.0896以下,相关系数(NC)在0.9708以上.本算法对噪声干扰、低通滤波、重采样、重量化、剪切、压缩等常见的攻击方法具有良好的鲁棒性.     

Passive scalars,three-dimensional volume-preserving maps,and chaos

The dynamics of a medium-sized particle (passive scalar) suspended in a general time-periodic incompressible fluid flow can be described by three-dimensional volume-preserving maps. In this paper, these maps are studied in limiting cases in which some of the variables change very little in each iteration and others change quite a lot. The former are called slow variables or actions, the latter fast variables or angles. The maps are classified by their number of actions. For maps with only one action we find strong evidence for the existence of invariant surfaces that survive the nonlinear perturbation in a KAM-like way. On the other hand, for the two-action case the motion is confined to invariant lines that break for arbitrary small size of the nonlinearity. Instead, we find that adiabatic invariant surfaces emerge and typically intersect the resonance sheet of the fast motion. At these intersections surfaces are locally broken and transitions from one to another can occur. We call this process, which is analogous to Arnold diffusion, singularity-induced diffusion. It is characteristic of two-action maps. In one-action maps, this diffusion is blocked by KAM-like surfaces.On leave of absence from the Departamento de Fisica, Universidad Nacional de La Plata, (1990), La Plata, Argentina.     

Valuations and multiplier ideals

We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are a formula for the complex integrability exponent of a plurisubharmonic function in terms of Kiselman numbers, and a proof of the openness conjecture by Demailly and Kollár. Our technique also yields new proofs of two recent results: one on the structure of the set of complex singularity exponents for holomorphic functions; the other by Lipman and Watanabe on the realization of ideals as multiplier ideals.

     

一种基于DCT变换的自适应彩色图像水印算法

提出了一种基于离散余弦变换的彩色图像数字水印算法.首先原始彩色图像的绿色分量进行8 x 8分块DCT变换.计算每块的噪声阈值,相应调整每块选取的两个中频系数的大小,把经过Arnold置乱加密的二值水印图像嵌入.水印提取时,不需要原始图像.实验结果表明,该算法能有效抵抗JPEG压缩、裁剪、加噪、图像增强等攻击,具有良好的透明性和较强的稳健性.