对数曲线

Elliptic curve cryptograph is based on the difficulty of solving discrete logarithm on elliptic curve domain, and therefore it has higher security than other cryptography.

椭圆曲线密码机制是基于椭圆曲线域上求离散对数难度，因此具有更高的安全性。

Its security depends not only on the elliptic curve discrete logarithms but also on the choice of the elliptic curve and its system.

其安全性不仅依赖于椭圆曲线离散对数的分解难度，而且依赖于椭圆曲线的选取和椭圆曲线密码体制。

In 1989, Neal Koblitz proposed the hyperelliptic curve cryptosystems as a natural generalization of ECC. HCC is based on the discrete logarithm problem on the Jacobian of hyperelliptic curves over finite fields.

作为椭圆曲线的一个推广，Neal Koblitz在1989年提出了超椭圆曲线密码体制，它是基于有限域上超椭圆曲线的Jacobian上的离散对数问题。D。

In 1989, Neal Koblitz proposed the hyperelliptic curve cryptosystems as anatural generalization of ECC. HCC is based on the discrete logarithm problem on theJacobian of hyperelliptic curves over finite fields.

作为椭圆曲线的一个推广，Neal Koblitz在1989年提出了超椭圆曲线密码体制，它是基于有限域上超椭圆曲线的Jacobian上的离散对数问题。D。

The automatic generation of logarithmic spiral is achieved by means of the language of VBA embedded in AutoCAD.

提出铲齿成形铣刀齿背曲线的最佳线形应是对数螺线，而后运用AutoCAD的内嵌编程语言VBA，实现了对数螺线齿背曲线的自动生成。

In order to improve the security, a signature scheme based on two hard problem assumptions is proposed. The security of the scheme is based on the difficulties of simultaneously solving the elliptic curve and quadratic residue. A attacker can't forge the signature of messages even if a attacker can solve theelliptic curve discrete logarithm problems or quadratic residue problem in the scheme.

为了提高签名的安全性，本文对Wang等人提出的签名方案进行改进，提出了一个基于椭圆曲线离散对数问题和二次剩余问题的数字签名方案，并对该方案的安全性进行分析，指出在椭圆曲线离散对数问题或二次剩余问题可解的情况下，攻击者也无法伪造消息的签名。

The fusant F-K6-lm4208 can't make gelatin liquefy,but can hydrogenize the nitrate,and ferment maltose, xylose, glucose, fructose, cellobiose, lactose, glucopyranoside, sorbose and mannose,but can't ferment rhamnose,aesculin and salicin.

对本实验室保存的反刍兽月形单胞菌K6及分离鉴定的粘膜乳杆菌lm4208进行了菌株生长曲线绘制，确定了粘膜乳杆菌lm4208及反刍兽月形单胞菌K6的对数生长期，粘膜乳杆菌lm4208对数生长期为4~12h，反刍兽月形单胞菌K6对数生长期为8~16h。

Three kinds of BCRC No.51534, 10322 and 10675 would be selected and acted as an experimental sample of Escherichia coli. Results shows that Escherichia coli of No.51534 will appear better performance because the maximum of open circuit voltage, closed current and power density are 1.01V, 22mA and 1342mW/m2, respectively. Concerning the effect of culture time with respect to different phase type on the electricity performance of MFCs, the time points on the intersection between lag phase and logarithmic phase, the middle of point of stationary phase for growth curve of Escherichia coli would appear a good performance of MFCs. In addition, the BCRC No. 51534 Escherichia coli possessing a better performance of MFCs than others would be suggested and applied to further studying. Comparison with the performance of MFCs with respect to electron mediator under different mole number, result shows that electron mediator of methylene blue with 4.63mM would appear a better electricity performance of MFCs than others. Concerning the different material of proton exchange membrane with PTFE-Nafion, Nafion 211, 212 and 117 with respect to the performance of MFCs, result shows that the Nafion 117 applied in MFCs will have a better performance of MFCs than other cases. Finally, the effect of molar concentration on the performance of MFCs would be expected at the studied cases of 0.4M, 0.2M, 0.1M and 0.05M respectively for cathode oxidant, result shows that a good performance of MFCs will happen at the condition of 0.2M. Those observations will be useful to improvement of MFCs in the further study.

於上述电池系统条件下，进行大肠杆菌生长曲线、电子传递介质、质子交换膜、电极与阴极氧化剂对电池电性效能分析；选择编号10322、10675与51534之大肠杆菌为实验菌株，依定量培养之生长曲线取出代表不同时生长特性时期的培养时间，利用亚甲基蓝作为电子传递介质进行实验分析从所测得的电量进行分析，以编号51534之大肠杆菌的微生物燃料电池有最大的开路电压为1.01V及最大闭路电流为22mA；当极化曲线中电压为0.47V、电流为11.4 mA时有最大的功率密度为1342 mW/m2；加以负载有平均工作功率密度294 mW/m2；从生长曲线与电性效能来分析，得知生长曲线的迟滞期与对数期的转变点与静止期的中间点有最佳电性效能表现；对於加入不同莫耳数之电子传递介质methylene blue、neutral red与thionine之电池效能表现，则以加入4.63mM methylene blue电子传递介质的电池有较佳平均功率密度230 mW/m2；另对於质子交换膜PTFE-Nafion、Nafion 211、Nafion 212与Nafion 117之电池效能表现，以Nafion 117质子交换膜的电池有较佳平均功率密度340 mW/m2；对於分析加入不同莫耳数浓度0.4M、0.2M、0.1M与0.05M的阴极氧化剂之电池效能，则以0.2M的阴极氧化剂的电池可得到较佳平均功率密度429 mW/m2。

Analyzed some correlation problem of using elliptic curve construct cryptosystem.Make the correlation counterchange on the elliptic curve that suitable for constructing the cryptosystem and the op eration on it. Analyzed and researched discrete logarithm problems of elliptic c urve suitable for cryptosystem.

文中分析研究了利用有限域上的椭圆曲线构建密码体制的相关问题，对于适于建立密码体制的一类椭圆曲线进行了相应的仿射代换和其运算的映射变换，对椭圆曲线构建密码体制的椭圆离散对数问题进行了分析研究。

Giving examples of its application in the design of curve eccentric clamp mechanism s, circular wedgy scarf joints and relieving shaped cutters and so on, this paper illuminates its application prospect in many fields of mechanical design and manufacturing engineering.

在给出对数螺线定义及其特有性质的基础上，探讨了对数螺线的美学价值。由此出发，以对数螺线在曲线偏心夹紧机构设计、圆楔面联接、铲齿成形刀具等方面的应用为例，阐明了它在机械设计与制造工程领域中的应用前景

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。