Fixed points of the RSA encryption algorithm

In this paper the problem of the number of fixed points for an RSA algorithm is considered. This is an important question from the point of view of any cryptosystem. We have estimated the expected value of this number for randomly chosen RSA parameters. It turned out that it is O(ln²n), and the probability of finding such a point is O(ln²n/n). Thus, these values are really negligible, which had been intuitively expected.     

基于整数的全同态加密体制的研究

DGHV体制是在对Gentry的基于理想格的全同态加密体制进行简化的基础上提出的,但该体制仅能对单比特的明文的加解密,并且效率不够高。2013年,Jean—Sebastien等人对DGHV体制进行了改进,完成了对明文序列的加解密。本文以改进的DGHV算法为基础,分析了改进DGHV算法的思路和方法,并对相应的压缩算法和自举算法进行了分析,给出了正确性证明和安全性证明,最后指出了改进的DGHV算法的主要优势。     

Algorithms for computing triangular decomposition of polynomial systems

We discuss algorithmic advances which have extended the pioneer work of Wu on triangular decompositions. We start with an overview of the key ideas which have led to either better implementation techniques or a better understanding of the underlying theory. We then present new techniques that we regard as essential to the recent success and for future research directions in the development of triangular decomposition methods.     

对多项式的欧几里德算法的改进

本文对用于求两个多项式的最大公约多项式的欧几里德算法作了改进，主要改进了决定该算法计算复杂性的ＥＭＧＣＤ的递归过程。通过计算复杂性的分析，改进算法比原算法快了一倍，而且提高了计算精度。     

基于灰色关联度和理想解法的输电网规划综合决策研究

提出基于灰色关联度和理想解法相结合处理输电网规划决策的方法,该方法通过在传统的理想解法中引入灰色关联度的概念,将欧式距离与灰色关联度有机结合,针对输电网规划决策中常常出现难以决策各个方案优劣的问题,构造了一种新的相对贴近度来决策方案的优劣,克服了使用单一方法造成决策问题主客观因素考虑不够全面所造成的误差,增强了对输电网规划方案评价结果的可信度。     

基于Dixon结式的一种九杆巴氏桁架位移分析

将Dixon结式运用到平面基本运动链的位移分析中,完成了一种两耦合度九杆巴氏桁架的位移分析。结合矢量法和复数法建立4个几何约束方程式,使用Dixon结式构造22×22的Dixon矩阵,提取公因式后将矩阵的行列式展开得到一元六十次多项式方程,回代过程中去掉4组增根得到56组解。为了对结果进行验证,同时使用同伦连续法对一个数字算例进行计算,两种方法得到的结果一致,说明这种巴氏桁架的装配构型数目最大值是56。     

Sequencing Analysis of a 36·8 kb Fragment of Yeast Chromosome XV Reveals 26 Open Reading Frames Including SEC63, CDC31, SUG2, GCD1, RBL2, PNT1, PAC1 and VPH1

The complete sequence of a 36 775 bp DNA segment located on the right arm of chromosome XV of Saccharomyces cerevisiae has been determined and analysed. The sequence encodes 26 open reading frames of at least 100 amino acids. Eight of these correspond to known genes, whereas 18 correspond to new genes. The sequence has been deposited in the EMBL databank under Accession Numbers: Z75154, Z75155, Z75156, Z75157, Z75158, Z75159, Z75160, Z75161, Z75162, Z75163, Z75164, Z75165, Z75166, Z75167, Z75168, Z75169, Z75170, Z75171, Z75172, Z75173, Z75174, Z75175, Z75176, Z75177, Z75178, Z75179. © 1997 John Wiley & Sons, Ltd.     

Robust event correlation scheme for fault identification in communication networks

The complexity of communication networks and the amount of information transferred in these networks have made the management of such networks increasingly difficult. Since faults are inevitable, quick detection, identification, and recovery are crucial to make the systems more robust and their operation more reliable. This paper proposes a novel event correlation scheme for fault identification in communication networks. This scheme is based on the algebraic operations of sets. The causality graph model is used to describe the cause‐and‐effect relationships between network events. For each disorder, and each manifestation, a unique prime number is assigned. The use of the greatest common devisor (GCD) makes the correlation process simple and fast. A simulation model is developed to verify the effectiveness and efficiency of the proposed scheme. From simulation results, we notice that this scheme not only identifies multiple disorders at one time but also is insensitive to noise. The time complexity of the correlation process is close to a function of n, where n is the number of observed manifestations, with order O(n²); therefore, the on‐line fault identification is easy to achieve. Copyright © 1999 John Wiley & Sons, Ltd.     

Sequencing analysis of a 40·2 kb fragment of yeast chromosome X reveals 19 open reading frames including URA2 (5′ end), TRK1, PBS2, SPT10, GCD14, RPE1, PHO86, NCA3, ASF1, CCT7, GZF3, two tRNA genes,three remnant delta elements and a Ty4 transposon

The complete sequence of a 40 247 bp DNA segment located on the left arm of chromosome X of Saccharomyces cerevisiae has been determined and analysed. The sequence encodes the 5′ coding region of the URA2 gene and 18 open reading frames of at least 100 amino acids. Ten of these correspond to known genes, whereas eight correspond to new genes. In addition, the sequence contains a tRNA-Ala gene, a tRNA-Asp gene, a Ty4 transposable element and three delta elements. The sequence has been deposited in the EMBL databank under Accession Numbers: Z49405, Z49404, Z49403, Z49402, Z49401, Z49400, Z49399, Z49398, Z49397, Z49396, Z49394, Z49392, Z49391, Z49390, Z49389, Z49387, Z49386, Z49385.     

Multiple Segment Line Scan-conversion

We present a new method for scan-converting a straight line. A scan-converted straight line may contain many pixel segments of identical shapes. Therefore, instead of scan-converting the whole line step by step, we can scan-convert multiple segments of a line through copying and replicating. With a few modifications to the existing algorithms, we can significantly speed up the scan-conversion process. The algorithm can be implemented in the hardware, further speeding up the process. The hardware design for the new algorithm is provided. We prove that we can speed up all existing line scan-conversion algorithms on the average 3 times.