位运算

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。

The software can achieve up to 15 decimal arithmetic, hex...

本软件可以实现多达15位十进制数的运算，十六进制的计算则可以实现12位的运算。

In this paper we will use the concept of "mutual opposite form" to simultaneously recode two scalars stating at most significant bit to least significant bit, i.e. left-to-right recoding. We propose a new representation with low joint Hamming weight to reduce the number of elliptic curve point additions to achieve decreasing the operation cost.

本文将透过符号交替表示式，针对两纯量从最高有效位元(most significant bit， MSB)编码至最低有效位元(least significant bit， LSB)以同步的方式重新编码，新的表示式具有低结合汉明权重特性，可以减少椭圆曲线点加法运算次数，达到降低运算成本的目的。

The three states are transformed via two-dimension liquid crystal element and polarizators, and ternary arithmetic operation and ternary logic al calculus completed directly in this way.

三值光计算机用相互垂直的两个线偏振光和零光强三个独立的光状态表示信息；用二维液晶器件和偏振器实现此三个状态间的转换；采用三进制算术运算；直接处理三值逻辑运算；拥有巨大的数据位数(容易超过10~4位)；具有光运算、光传送、电控制等结构特色，具有很强的空间、时间并行性。

The algorithm splits the original image to some blockes and do DCT transform,chooses three low-frequency coefficients in every block,quantizes them and chooses the least significance bits,then does the xor operations with the corresponding bits of water mark.,the result is the key.At the same time,we choose three high-frequency,and do the same operation and generate the other key.

该方法对原始图像进行分块DCT变换，每块取三个DCT低频系数，把这三个系数量化后取最低有效位，与水印的对应位进行异或运算得到密钥；再取三个高频系数进行异或等运算得到另一密钥。

At last, it"s studied the consistency of unsigned ones complement addition with bit-wise exclusive-OR and addition modulo 2". The formula of consistency probability is proposed.

随后，本文研究了进位返加运算与逐位模2加运算及模2~n加运算的相容性问题，给出了其相容概率的计算公式。

The main technique applied in our method is derived from the features of the eight bit-planes of a gray image. The XOR bit-wise operation is used for two bit pixels among the neighboring bit-planes from the most significant bit to the least significant bit.

本提出方法是将欲隐藏之灰阶影像分解成八张位元平面，并利用其影像前几个位元平面0与1分布会有群聚现象，将两两位元平面间作XOR (Exclusive-or)运算，再使用线性四元树的观念将运算后的资料进行有效BFS编码，之后再隐藏於伪装图之像素最低位元，使最后藏入资料的伪装图影像仍呈现高度清晰的图像显示，也就是说PSNR的测度皆能远大於30dB。

The crossover operation in the traditional GA operating is that choose two chromosome cross only at random also you can cross a bit, match and cross partly, cross order and cross cycle etc.

传统GA算法中的交叉操作，是随机选取两个染色体进行单点交叉(也可以多点交叉、部分匹配交叉、顺序交叉和周期交叉等等)，但是不管是采用何种交叉操作，新的子代染色体某一基因位上的值都是由两个父代染色体中相应基因位值经过一定交叉运算(直接交换或经算术运算等)所得到的，采用这种交叉算子操作使群体经过多次迭代后群体中的个体开始出现极大的相似性，因此照此下去就会出现早期收敛现象，使得算法的收敛速度非常慢甚至只能求到问题的局部最优解。

The crossover operation in the traditional GA operating is that choose two chromosome cross only at random also you can cross a bit, match and cross partly, cross order and cross cycle etc.

传统GA算法中的交*操作，是随机选取两个染色体进行单点交*(也可以多点交*、部分匹配交*、顺序交*和周期交*等等)，但是不管是采用何种交*操作，新的子代染色体某一基因位上的值都是由两个父代染色体中相应基因位值经过一定交*运算(直接交换或经算术运算等)所得到的，采用这种交*算子操作使群体经过多次迭代后群体中的个体开始出现极大的相似性，因此照此下去就会出现早期收敛现象，使得算法的收敛速度非常慢甚至只能求到问题的局部最优解。

The pipelined CORDIC architecture is very suitable for FFT butterfly operation because of its high throughput and regularity, but it will consume lots of resources,this article presents an improved architecture of CORDIC pipeline,starting with the property that the FFT rotary factor is fixed but not arbitrary,and according to the mapping between the basic rotational angle of CORDIC and scale factor and the rule for transform among the scale factors.On the condition that the velocity of FFT butterfly operati...

CORDIC流水线结构因其高吞吐率及规整性，而很适合于FFT蝶形运算，但其缺点是耗资源多，本文从FFT中旋转因子固定不任意的特点出发，根据CORDIC基本旋转角度与缩放因子的对应关系和缩放因子之间的转换规律，对CORDIC流水线结构进行了改进，在蝶形运算速度不变的情况下，进一步减少所耗资源，在字长为16位的FFT中，每个旋转因子可用25位的控制序列来替代，从而使每个旋转因子的存储空间由32位减少到25位。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。