始于凸包络线的闭主曲线学习算法研究

本文提出了将凸包技术与自组织拓扑映射技术相结合的一种针对封闭曲线特征提取的主曲线学习算法，解决了一般主曲线算法无法有效模拟封闭和较为复杂分布数据集的难题。算法以数据集的凸包络线为起始步，通过分析数据集的全局和局部特征，逐步逼近数据集分布并获得封闭主曲线。算法的关键在于凹点挖掘算法的研究。实验结果表明，对于一般封闭曲线点集，该方法均能在较短的时间步内较好地逼近源数据集。该算法结构简单，复杂性在最坏情况下也不超过Ｏ（n^2），同时对图像的有界连通区域外部边界特征的提取与图形识别亦将具有较高的应用价值。     

基于混沌与椭圆曲线的安全电子邮件系统

PEM、PGP以及S/MIME虽然提高了电子邮件的安全性，但仍存在速度慢以及安全性不够等不足。该文在介绍了混沌的分组密码算法、二维超混沌的单向Hash函数以及混沌与椭圆曲线的数字签名算法的基础上，提出了一种新的安全电子邮件系统。分析和应用表明，该系统具较高的速度和良好的安全性，具有广泛的应用前景。     

主曲线算法初始值选取的分析

主曲线是一种用于数据压缩和特征提取的有效方法，是对主成分分析的非线性推广。由于主曲线与主成分的密切联系，主曲线生成算法通常以第二主成分线做初始值。然而实验发现第一主成分未必是算法初始化的最佳选择。本文将以HS算法和多边形算法为例，就初始值的选取对生成主曲线的影响做出分析并通过实验得出结论：HS算法以原点作初值效果较好，多边彤算法应根据数据点集的不同结构选择合适的初值。     

基于椭圆曲线的单轮零知识证明方案

零知识证明在信息安全领域有着很广泛的应用前景。然而传统的零知识证明方案为了保证方案的正确性需要多轮的迭代,大大增加了交互双方的通信量,使得方案往往不适合实际应用。提出了一种单轮零知识证明的方案,在保证方案正确性、完全性和零知识性的同时将方案运行的迭代次数降低到1,最大程度地减少了方案的通信量。同时将零知识证明扩展到了椭圆曲线上的离散对数问题,提高了方案的安全性。最后给出了构造单轮零知识方案的一个必要条件。     

Fingerprint minutiae extraction based on principal curves

It is important to extract minutiae of a fingerprint for the implementation of an auto fingerprint identification system. In this paper, the principal graph algorithm proposed by Kegl is used to obtain principal curves, which can be served as the skeletons of a fingerprint. Based on the obtained principal curves, a minutiae extraction algorithm is proposed to extract minutiae of the fingerprint. The experimental results indicate that principal curves obtained from the principal graph algorithm are smoother than the ones obtained from thinning algorithm, and the minutiae extracted by the proposed algorithm are more efficient.     

基于Poisson方程的曲线形状渐变方法

以定义在分段线性曲线上的离散Poisson方程为理论基础,提出了一种同时适用于平面和空间曲线形状渐变的方法.通过在源曲线和目标曲线上定义局部标架,给出了一种非线性梯度场插值算法,使得源曲线的梯度场逐步过渡到目标曲线的梯度场,所得到的中间梯度场与用户指定的关键节点路径一起输入离散Poisson方程求解得到渐变序列 .该方法不直接插值顶点坐标,而是将源曲线与目标曲线视为定义在公共定义域上的标量场,并在梯度域进行梯度场操纵.对中间帧曲线周长以及平面曲线所包围的内部面积变化的统计表明:该算法尽可能地保持了几何形状的刚性,在中间帧求解的稳定性方面该算法优于同类其他方法.     

A CNC machine tool interpolator for surfaces of cross-sectional design

A machining strategy for milling a particular set of surfaces, obtained by the technique of cross-sectional design is proposed. The surfaces considered are formed by sliding a Bezier curve (profile curve) along another Bezier curve (trajectory curve). The curves are located in perpendicular planes. The method employs a three-axis CNC milling machine equipped with suitable ball-end cutter and is based on the locus-tracing concept. The algorithm described, utilizes a real-time CNC interpolator providing the highest possible accuracy, of which the milling machine is capable. The surface quality is controlled by keeping the distance between scallops within a programmed value. Finally, the whole machining task can be programmed in a single block of the part program.     

椭圆曲线Menezes-Vanstone加密体制的改进与实现

椭圆曲线密码体制ECC(Elliptic Curves Cryptosystem)是目前加密领域中最重要的密码体制之一,而Menezes-Vanstone密码算法是ECC中一种实用的加密算法.本文通过改进Menezes-Vanstone密码算法,提出一种更实用的椭圆曲线加密体制,从而更有效、快速实现了网络通信中数据的安全保密性     

基于超椭圆曲线密码的多方授权签名方案

分析了现有电子商务、电子政务多方授权方案及网络通信中的多重数字签名协议，基于超椭圆曲线密码，针对现有多重签名方案存在秘密信息泄漏、签名伪造等安全漏洞及协议过程复杂、签名认证运算开销大等不足之处，该文提出了一类混合多重签名方案，分析了方案的安全性与执行效率。该协议和算法安全、简洁、高效，降低了软硬件实现的系统开销，可广泛地应用于计算机与无线通信等网络 环境。     

Interpolation by geometric algorithm

We present a novel geometric algorithm to construct a smooth surface that interpolates a triangular or a quadrilateral mesh of arbitrary topological type formed by n vertices. Although our method can be applied to B-spline surfaces and subdivision surfaces of all kinds, we illustrate our algorithm focusing on Loop subdivision surfaces as most of the meshes are in triangular form. We start our algorithm by assuming that the given triangular mesh is a control net of a Loop subdivision surface. The control points are iteratively updated globally by a simple local point-surface distance computation and an offsetting procedure without solving a linear system. The complexity of our algorithm is O(mn) where n is the number of vertices and m is the number of iterations. The number of iterations m depends on the fineness of the mesh and accuracy required.