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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。
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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。
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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。
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A series of reactions may occur when the nitrous acid and naphthalene inside the atmospheric aqueous phases is exposed to sunlight. This article devotes to investigating from a microscopic angle the reaction mechanism and kinetics of this system using laser flash photolysis technique with an excitation wavelength of 355nm. The main research results are listed as below:(1) The OH quantum yield FOH for the photolysis of HNO2 in the aqueous phase was determined to be 0.234 and the absorption spectrum of OH radical was recorded as well.
本文以激光闪光光解为主要研究手段,考察了大气液滴中的HNO2及HNO2+萘体系经355nm紫外光照射后发生的微观反应及其机理,结果表明:(1)液滴中的HNO2经355nm光照产生OH自由基的量子产额为FOH=0.234;以瞬态技术记录了水相中的OH自由基的吸收光谱。
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Sexual behaviors that occur during sleep range from simple moaning to fondling to outright intercourse, scientists say.
专家说,发生在睡梦中的性行为从简单的呻吟、抚摸到直接的性行为。
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Scientists at The Forsyth Institute have discovered that some cells have to die for regeneration to occur.
最近Forsyth研究所研究人员发现,为了实现再生,有些细胞必须死亡。
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Such as the West Fourth Ring定慧寺the乐府江南bridge, combined with the geographic location of natural advantages, the design of the garden, to absorb China's Jiangnan garden style of gardening techniques and the experience of the North, to build the capital charm unique, scenic spots occur repeatedly landscape south of the Yangtze River, in the master plan for 300,000 square meters of land, there are nearly 10 more than 200 30 ~ 100 years of natural trees scattered into the garden, including gingko, cedar, gold tree, acacia, Pentagon Maple and so on.
如西四环定慧寺桥的乐府江南,加上地理位置优越的自然条件,设计中的花园,吸收中国的江南园林风格的园艺技术和经验,北至首都建设魅力独特,风景名胜区不断发生的景观江南,在总计划的30万平方米的土地,有近10 200多名30 100年的自然树木散布到花园,包括银杏,雪松,黄金树,台湾相思,五角大楼枫树等。
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Keep in touch with what's going on in the organization as a whole so you can be more informed when meetings occur. Pick up the phone and give someone else a call to see what you can learn, or take a stroll through different parts of the workplace to find out what others are up to.
保持和公司整体进展同步,你就可以更好的知道什么时候有会议,拿起话筒给其他人打个电话,看看你可以了解到什么,或者到公司其他地方走走,看看其他人怎么样了。
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China 's leaders are not accustomed to protests and go to great lengths to see that they do not occur while they are abroad.
中国领导人不习惯抗议行为,而且想方设法让这种情况不会在他们出访时出现。
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There appears to be a strong synergy between these two hormones here, such that gynecomastia might even be able to occur with the help of progestins, without excessive estrogen levels being necessary.
现在似乎有一种强大的协同作用这两个激素在这里,这样,乳房甚至可能能够发生的帮助下,孕,没有过多的雌激素水平的必要。
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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。
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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。
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When I was in school, the rabbi explained everythingin the Bible two different ways.
当我上学的时候,老师解释《圣经》用两种不同的方法。