NTRU公开密钥体制算法分析与实现

介绍了一种新的公开密钥体制NTRU。NTRU逄法的安全性取决于一从一个非常大的维数格中寻找很短向量的困难性，NTRU公开密钥体制算法主要计算对象是对多项式进行加、减、乘、模等运算。用NTRU产生的密钥方法比较容易，加密、解密的速度比RSA等著名算法快得多。从安全笥和有效性方面分析，NTRU密码体制有着广阔的应用前景。     

NTRU中间距失败的概率分析及其影响

NTRU是一种极有发展潜力的公钥密码体制,然而它的解密机制是不完善的,可能出现合法密文无法解密的现象,这严重影响了该体制的安全性.间距失败是导致解密失败的一个重要原因,对此,在p=2相关多项式均为系数为0或1的二元多项式条件下,讨论了卷积系数的弱线性相关性,在此基础上对间距失败的概率计算进行了介绍和分析,得到了相关的计算公式,并介绍了一种利用间距失败对NTRU的攻击方法.     

NTRU中多项式的逆问题

在NTRU公钥密码体制中,一个多项式是否有逆多项式是一个很重要的问题.本文介绍了NTRU公钥密码体制,给出了NTRU中多项式是否有逆的判定定理,并对所提出的定理进行了相应的证明.最后我们用例子来说明怎样运用该判定定理,给出了求解多项式逆的算法.     

基于自组装DNA计算的NTRU密码系统破译方案(英文)

自组装DNA计算在解决NP问题,尤其在破译密码系统方面,具有传统计算机无法比拟的优势．文中提出了一种用自组装DNA计算破译NTRU公钥密码系统的方法．针对NTRU密码系统的特点,采用DNA瓦片编码信息,借助于瓦片间的粘性末端进行自组装,给出了求解多项式卷积运算的实现方案．在此基础上,通过引入非确定性的指派瓦片,提出了一种破译NTRU系统的非确定性算法．通过创建数以亿计的参与计算的DNA瓦片,该算法可以并行地测试每个可能的密钥,以高概率地输出正确密钥．该方法最大的优点是充分利用了DNA瓦片具有的海量存储能力、生化反应的巨大并行性以及组装的自发有序性．理论分析表明,该方法具有一定的可行性．     

基于双重优化的卷积神经网络图像识别算法*

为了进一步提高卷积神经网络算法的收敛速度和识别精度,提出基于双重优化的卷积神经网络图像识别算法。在构建卷积神经网络的过程中,针对特征提取和回归分类建立双重优化模型,实现对卷积与全连接过程的集成优化,并与局部优化算法对比,分析各算法的识别率和收敛速度的差异。在手写数字集和人脸数据集上的实验表明,双重优化模型可以在较大程度上提高卷积神经网络的收敛速度和识别精度,并且这种优化策略可以进一步拓展到其它与卷积神经网络相关的深度学习算法中。     

基于NTRU的多密钥同态加密方案解密结构

为了进一步提升NTRU型多密钥全同态加密（MKFHE）方案的安全性和效率,基于素数幂次分圆多项式环,研究了NTRU型多密钥同态加密的原始解密结构特点,并提出了两种多密钥同态解密结构改进优化方法。首先通过降低多项式系数,设计了“Regev-Style”多密钥解密结构;其次通过扩展密文维度,设计了“Ciphertext-Expansion”多密钥解密结构。通过与NTRU型多密钥同态加密方案的原始解密结构进行对比分析,结果表明“Regev-Style”多密钥解密结构降低了产生噪声的量级,用于NTRU型多密钥全同态加密方案设计时能减少密钥交换次数和模交换次数;“Ciphertext-Expansion”多密钥解密结构消除了密钥交换过程,降低了产生噪声的量级,且能更有效地处理重复用户的密文乘积。改进优化的多密钥解密结构的安全性均基于素数幂次分圆多项式环上的误差学习（LWE）问题和判定小多项式比（DSPR）假设,这些结构能较好地抵御子域攻击。通过选取合适的参数,它们可用于设计更加安全高效的NTRU型多密钥全同态加密方案。     

NTRU的有效实现方案研究

NTRU是Jeffrey Hoffstein等在1996年提出的一种新的公钥密码体制,其安全性基于大维数格中寻找最短向量的数学难题.NTRU公开密钥体制算法主要对象是对N-1次多项式进行加、减、乘、模运算,所以该加密解密的速度比RSA等著名算法快得多,和椭圆曲线密码体制一起,成为新一代最优秀的公钥密码体制.对NTRU的设计原理以独特的思维方法进行了分析,并对主要算法进行了优化设计和实现分析.特别地,给出了算法的优化分析及完整实现方案,大大提高了系统的性能.     

一种优化的NTRU算法

NTRU算法是至今为止最快的公钥密码体制,它的安全性是基于在非常大的维数格中寻找最短向量的困难性。为了增强NTRU算法的速度和效率,本文介绍了NTRU的优化算法及与原始算法的比较。     

NTRU算法的分析

介绍了一种新的公开密钥体制NTRU算法,NTRU算法的安全性是基于数论中在一个非常大的维效格中寻找一个很短向量的数学难 题。NTRU算法与RSA等算法相比具有更高的运算速度,更快的密钥生成速度和更少的存储空间,尽管在安全性方面与RSA相比有一些缺陷, 但也有弥补的方法,因此NTRU算法将会有更广阔的应用前景。     

一种优化NTRU公钥密码体制

主要阐述了一个优化的NTRU公钥密码体制。通过对参数的选取及多项式的优化改进,这个优化的NTRU公钥密码体制与原体制及其他公钥密码体制相比较具有如下优点:算法更加简洁,密钥的生成简单。优化后的算法保留了原有的优点,同时加、解密速度提高了,其抗攻击能力也有明显的提高。此方案将有很好的研究价值与应用前景。     

Fast Recursive Computation of Krawtchouk Polynomials

Krawtchouk polynomials (KPs) and their moments are used widely in the field of signal processing for their superior discriminatory properties. This study proposes a new fast recursive algorithm to compute Krawtchouk polynomial coefficients (KPCs). This algorithm is based on the symmetry property of KPCs along the primary and secondary diagonals of the polynomial array. The \(n-x\) plane of the KP array is partitioned into four triangles, which are symmetrical across the primary and secondary diagonals. The proposed algorithm computes the KPCs for only one triangle (partition), while the coefficients of the other three triangles (partitions) can be computed using the derived symmetry properties of the KP. Therefore, only N / 4 recursion times are required. The proposed algorithm can also be used to compute polynomial coefficients for different values of the parameter p in interval (0, 1). The performance of the proposed algorithm is compared with that in previous literature in terms of image reconstruction error, polynomial size, and computation cost. Moreover, the proposed algorithm is applied in a face recognition system to determine the impact of parameter p on feature extraction ability. Simulation results show that the proposed algorithm has a remarkable advantage over other existing algorithms for a wide range of parameters p and polynomial size N, especially in reducing the computation time and the number of operations utilized.     

采用牛顿插值的多项式因式分解算法的设计与实现

基于Kronecker所提供的一元多项式因式分解的构造算法、一元整系数多项式在整数环上因式分解理论,利用牛顿向前差分插值算法代替拉格朗日插值算法,把有理域上一元高次多项式因式分解化为在整数环上的因式分解,得到了整数环上的一元多项式因式分解的构造性算法,给出了具体实现过程。     

基于SA-WPSO的遥感图像校正方法

提出一种基于SA-WPSO的遥感图像校正方法。该方法利用多项式模型对图像进行初步几何校正,得到多项式校正系数后,将模拟退火(SA)思想引入粒子群优化(PSO)算法,通过改进的SA-WPSO算法优化多项式校正系数,在此基础上实现图像的几何校正。实验结果证明,与二次多项式及三次多项式校正方法相比,该方法的校正精度更高、鲁棒性更好。     

The root-locus method of synthesis of stable polynomials by adjustment of all coefficients

The problem of synthesis of an asymptotically stable polynomial on the basis of the initial unstable polynomial is solved. For the purpose of its solution, the notion of the extended (complete) root locus of a polynomial is introduced, which enables one to observe the dynamics of all its coefficients simultaneously, to isolate the root-locus trajectories, along which values of each coefficient change, to establish their interrelation, which provides a way of using these trajectories as “conductors” for the movement of roots in the desired domains. Values of the coefficients that ensure the stability of a polynomial are chosen from the stability intervals found on the stated trajectories as the nearest values to the values of appropriate coefficients of the unstable polynomial or by any other criterion, for example, the criterion of provision of the required stability reserve. The sphere of application of the root locus, which is conventionally used for synthesis of characteristic polynomials through the variation of only one parameter (coefficient) of the polynomial, is extended for the synthesis of polynomials by way of changing all coefficients and with many changing coefficients. Examples of application of the developed algorithm are considered for the synthesis of stable polynomials with constant and interval coefficients.     

Analysis of nonlinear electrical circuits using bernstein polynomials

In electrical circuit analysis, it is often necessary to find the set of all direct current (d.c.) operating points (either voltages or currents) of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.     

Generalized Subresultants for Computing the Smith Normal Form of Polynomial Matrices

We describe a new algorithm for the computation of the Smith normal form of polynomial matrices. This algorithm computes the normal form and pre- and post-multipliers in deterministic polynomial time. Noticing that the computation reduces to a linear algebra problem over the field of the coefficients, we obtain a good worst-case complexity bound.     

Formal Solutions of Linear Ordinary Differential Equations Containing m-Hypergeometric Series

Let a linear homogeneous ordinary differential equation with polynomial coefficients over a field be given. For a singular point of the equation, the fundamental system of formal solutions that contain a finite number of power series with coefficients belonging to the algebraic extension of can be constructed by known algorithms. In this paper, an algorithm is suggested for construction of a space of formal solutions such that all series containing in these solutions have m-hypergeometric coefficients. The implementation of the algorithm in the computer algebra system Maple is discussed.     

Closed forms for the Levinson coefficients of polynomialcompensators and inverse systems

The least-squares transformation of a discrete-time multivariable linear system into a desired system by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution of a normal linear matrix equation whose coefficients are shown to be the weighting patterns of certain linear systems. These can then be used in the recursive solution of the normal equation     

Analysis of CZCS data for the U.K. South-western Approaches

The implementation of a non-iterative atmospheric correction algorithm is described in detail and the performance of the algorithm is illustrated for several CZCS images. Chlorophyll retrieval is attempted using linear, power and polynomial regression for ratios of corrected images and the best correlation coefficients are in the region of 0-9. The same images are analysed in three spectral bands using the ISOCLS clustering algorithm and ocean areas are stratified into subclass patterns which correlate well with ratios and sea-truth. The monocluster blocks approach is used to extract training statistics for maximum likelihood classification of ocean areas and the results compare favourably with corresponding ratio images.