查询词典 number field

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

Zhang : I might be engaged in artistic creation for a longer period and seen relatively more in this field. As a teacher facing a great number of students I'm not able to rely on any means to point out a feasible as well as effective way because each individual has his or her own way to blaze.

张： 我可能从事艺术的时间更长一点，见的多一些，所以作为一个老师，我面对众多的学生没有办法通过某种方法给他们指出一条行之有效的路来，因为每个人都必须走一条自己的路。

Fermat s little theorem is one of the important theorems in number theory,but there has been little discussion in geometric field about it.

费马小定理是数论中的一个重要定理，但对其几何意义的论述几乎没有，给出了费马小定理的几何意义。

FA Campaign Plan, The first strategy to improve the FA Branch is to increase the flow; by this we mean increase the number and quality of officers choosing Field Artillery.

FA 行动计划，第一个改进野战炮兵的策略是增加人员流动性以提高选择野战炮兵的指挥员的数量和质量，同时增加数量。

We provide analysis on the principle of SISR, illustrate errors in real-world measurements, and demonstrate a working SISR implementation in field experiments on a test bed of 37 wireless nodes, as well as show the superior performance of SISR in simulation with a larger number of nodes.

我们分析了 SISR 的原理，举例说明在现实测量中的错误，证明了一个在真实环境中的野外现场试验，这个试验是 SISR 实现的，该试验含有37个无线节点，显示了在含有大量节点的大规模网络中 SISR 的高级特性。

With the increased number of individual employment in the exercise and fitness field, questions of quality control, legal liability, and ethics arises.

从事运动和体适能领域的从业人员数目渐增，品质的控制、合法性及职业道德的问题逐渐浮起。

Each officer carries swords, pistols, big dispatch cases, field glasses, canteens and other odds and ends in such number that he should have an entire compartment to himself.

每名警务人员进行刀剑，手枪，大调度情况下，外地的眼镜，食堂及其他什物在这样一些，他应该有一个自己整个舱室。

In our sales management, field hockey is very serious increase in the number of management costs, reduced sales force morale, and cultivate a culture of short-term speculation.

在我们的销售管理中，曲棍球现象非常严重，增加了很多管理成本，降低了销售队伍士气，养成了投机的短期文化。

Track and field, With the judge's order, the The number of viewers of heart, Then, Toward the market, Full of passion, Encouragement!

田径场上，随着裁判员的一声令下，多少观众的心，便，向着场上，激情满怀地，呐喊助威！

In SDF/CICS, a character used in the field definition function of the map editor to indicate that two adjacent fields should be separated according to the number of trailing blank characters in the line.

在客户信息控制系统屏幕定义程序中，用于映象编辑程序的字段定义功能中的一种字符，它根据一行中尾随的空格字符个数来分隔两个相邻字段。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。