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The ECC theory was studied in this paper. Polynomial was used to complete the hardware design of all kinds of algorithm including multiplication, division, point addition, point doubling和 point multiplication in GF (2m).

本文研究了椭圆曲线密码学理论,采用多项式基实现了椭圆曲线在有限域GF(2m)中各种运算的硬件设计,这些运算包括乘法、除法、点加、倍点和点乘,并用软硬件结合的方式实现了ECC的加/解密流程。

We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.

我们容易验证乘法满足结合律和交换律,并且由加法结果的唯一性得出乘法结果的唯一性和乘法消去律。

We cannot always have associative law for operations, for instance, we did not have this law for mixed addition and multiplication,neither for subtraction, 2+3 2+1≠(2+3)(2+1)=5 3,(2-3)- 2≠2-(3-2),this is why we have to set the rule in operations that "doing inside bracket at first and out side afterwards, doing multiplication and dividing first and addition and subtraction afterwards".

注意运算的结合律并不是永远对的,比如加法和乘法的混合运算就没有结合律,减法也没有,2+3 2+1≠5 3,(2-3)- 2≠2-(3-2),因此我们运算中总是规定先括号内再括号外,先加减后乘除。

To raise the efficiency of scalar multiplication on elliptic curve,a scalar multiplication algorithm based on double base number system over binary field was improved.

为了提高椭圆曲线标量乘法效率,对二元域上椭圆曲线的基于双基数的标量乘法进行改进。

Based on the point that there is something in common between the rules of matrix multiplication and the figure connection in braid multiplication, this paper gave a new representation of braid group called node matrix representation.

利用矩阵乘法规则与辫子乘法中图形的上下对应连接有类似之处这一特点,提出一种用结点矩阵表示辫子的方法。

Shoot apices of calla lily were used for in vitro culture. Multiplication rate on lateral bud formation was low. There were two patterns of multiplication rates with serial subcultures among three calla lily cultivars.

本研究以三个彩色海芋品种继代培养之培殖体及发根苗为材,调查续继代过程组培体增殖倍并探讨继代次对增殖族群主芽基部及发根苗基径大小频分布的影响。

A parallel algorithm for matrix multiplication is proposed according to the characteristic of matrix multiplication.

本文根据矩阵相乘的特点,提出了矩阵相乘的并行算法。

In comparison with traditional pipeline FFT, the complex multiplication was implemented by shifting and addition operations in order to eliminate multiplication unit and coefficient ROM.

与传统的流水线FFT比较,该模块中的复数乘法运算全部采用移位相加操作完成,因而消除了乘法器及旋转因子ROM的使用,降低了功耗。

Using bi-imaginary number representation, complex multiplication is simplified into two multiplication, instead of four ones in the previous method.

为克服空间带宽积的限制,提出了利用有限的外积乘法单元,通过矩阵分块和矢量循环流动进行任意维数矩阵与矢量运算算法,处理器利用率高。

By utilizing the complex multiplication property of the curves and using a modulo reduction and Frobenius expansion technique, it is shown that there is a fast point multiplication method without precomputation on the curves, which is 6 times faster than the ordinary repeated-double-add method.

结果显示,利用这类曲线的复乘性质,使用模约减和Frobenius展开技巧,这类曲线上存在一种不带预计算的快速点乘算法,其运算速度是通常的重复加倍-点加算法的6倍。

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