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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。

It is likely that more outbreaks will occur, FAO warned.

还可能会出现更多的疫情，粮农组织警告说。

Creativity and the creative process are hard to predict. Therefore, failure is going to occur . If there is a strong likelihood that your boss will criticize your "far-out"idea, you may not risk expressing it.

如果你有一个很好的想法并且有很大的可能性，但你的老板如果责备你的这个很有远见的想法，那么你可能不会冒险表达出来。

Astigmatism can occur in addition to nearsightedness and farsightedness.

散光可发生在除近视和远视。

The gain-frequency characteristic of the amplifier and its feedback network must be such that oscillation does not occur.

OP和其反馈网络的频率特性，必须保证不会产生震荡。

Tracksites occur exclusively throughout several stratigraphic levels of a thick, mixed-affinity, lagoonal-terrestrial sequence known as the Upper Red Formation in north central Iran and within a continental series deposited in the southern Caspian area in north of the country. The tracks from the Upper Red Formation are mainly artiodactylan type, attributed to several gazelle sized species due to their small size, and other tracks attributed to small, medium and large sized mustelid and felid carnivores.

足迹化石在伊朗中北部分布在一套被称为上红组的厚层、混杂的泻湖－陆相地层序列的数个层位中；在伊朗北部的里海地区南部，则位于一套陆相沉积序列中：产自上红组的足迹以偶蹄动物类型为主，由于个体很小，可归入几种像羚羊一样大小的种；其他足迹则分别归人小型、中型和大型的触科和猫科食肉动物。

It was thought that the mast important Fe sources occur in Precambrian BIFs. BIFs and ferruginous rock series in them contain abundant usable Au, Cu, Zn, Co and PGEs elements.

前寒武纪条带状铁建造中拥有全球最重要的铁矿资源，BIFs中以及包括BIFs在内的含铁岩系还含有丰富的金、铜、锌、钴、铂族等有用元素。

For the disease to occur, a sperm carrying the mutation (50:50 chance) must fertilise an egg carrying the mutation (50:50 chance).

为疾病的发生，精子进行基因突变（ 50：50机会）必须受精鸡蛋进行突变（ 50：50机会）。

This is the time when the sperm should arrive if a fertilization is to occur.

如果受精将要发生的话，这恰恰是精子应该抵达的时候。

About 15% of strokes occur in people with Atrial Fibrillation .

大约15%的中风发生在罹患心房纤维性颤动的人身上。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。