查询词典 S curve

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

Moreover, the curve of mixing energies△G_m at different surface compressure vs molar fraction of nervonic acid appeared a positive deviation comparing to the ideal mixing surplus energies△G_M~1 curve, which indicated a phase separation phenomena in the mixed monolayer.

此外，在不同表面压下的混合自由能ΔG_m对神经酸摩尔分数曲线与理想的混合过剩自由能ΔG_M~1曲线相比出现相似的正偏差，说明这种混合单分子膜出现了相分离现象。

The results showed that the cubic curve, inverted U-shaped EKC and the concave curve could be used to describe the relationship between environmental change and economic development in Henan province.

结果表明：河南省环境状况和经济发展之间呈现三次曲线、倒U形和"凹函数"和3种形式。

This blade has a gentle, sloping convex curve to the point versus the concave curve of the clip blade.

相对于回形刀刃的凹曲线而言，这种刀刃具有一条延伸到刀尖的、温和的凸斜率曲线。

It can be seen from the long time asymptotic solutions, that the pressure curve is a concave curve and ...

注稠化水等措施是改造这种油层的方向，但最终界限目前还不好确定。浊层研究、油田开发和各种油井工程措施应当考虑相对流动比这一因素。

If singular value curve is convex in the coordinates 'k' of maximum peak of curvature spectrum, then the number of effective singular values is k; if singular value curve is concave in the coordinates 'k', then the number of effective singular values is k-1, and this rule is tested by the signal processing examples.

如果奇异值曲线在曲率谱最大峰值的位置坐标k处是凸出的，则有效奇异值的个数为k；如果奇异值曲线在k处是凹进的，则有效奇异值的个数为k-1，通过信号处理实例证实了这种结论。

Chinese outline fonts ; curve ; concave point and convex point ; stroke extraction ; curve fitting.

汉字轮廓库； Bezier曲线；凹凸点；笔划抽取；曲线拟合

If the curve is concave, the highest curve that touches the budget constraint must be either on horizontal axis or vertical axis, and we call that "corner solution".

因为还可以把曲线再往右上方移，直到无差别曲线横轴或者纵轴相交的点刚好重合在 budget constraint上，那样才是最优。

To solve the coupled wave function of nonlinear recording hologram, the linearization method was advanced, and two modulating models of refractive index were adopted, the convex curve and the concave curve.

采用折射率调制特性为上凸型和下凹型的调制曲线，提出了线性化求解非线性记录全息图耦合波方程的方法。

Taking the reflective phase hologram grating as an example, the spectral properties of the gratings were analyzed, for recording material with refractivity modulated in the convex curve and concave curve, by the coupled-wave theory.

以反射相位型全息光栅为例，用耦合波理论分析计算了记录介质折射率调制为上凸型和下凹型调制曲线的体全息图的衍射光谱特性。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。