查询词典 scalar product

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。

In this equation,* is a scalar multiplication, x is a vector cross product, and .

在方程式中，"*"代表纯量乘法，"x"是矢量的叉积，而"。"

If two vectors are associated with each other as a dot product, the result is a scalar.

如果两个向量以标量积结合，其结果为一标量。

Since scalars are independent of the coordinate system, the dot product of two vectors is called a scalar invariant

因为标量与坐标系无关，故两个矢量的点积称为标量不变量。

The volume V is given in terms of the scalar triple product.

体积V能用数量三乘积表示。

The scalar triple product, the determinant of the matrix formed by columns A, B, C.

前两个矢量点积后于第三个矢量叉乘，或是由列A，B，C所构成矩阵的行列式值。

Defined the nodal velocity on the moving interface of theALE mesh as a product of a scalar and a shape vector, the kinematical boundary con-ditions on the free surface is modified to increase the freedom of the movements of thegrid on free interface.

将ALE网格运动界面节点的速度定义为一个标量和形状向量的乘积，用它修正自由液面网格速度与流场速度关系式，以增加自由面网格节点运动的自由度。

The dot product, being the product of three scalars, is a scalar.

点积是三个标量的乘积，所以是个标量。

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。