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.

本文介紹了計(jì)算有限域上橢圓曲線群的階的Schoof-Elkies-Atkin算法，在具體處理算法過程中18岁以下禁视频免费网站，我們給出了計(jì)算除多項(xiàng)式f〓的快速算法和尋找2〓階本原點(diǎn)的快速算法3344视频；標(biāo)量乘法是有關(guān)橢圓曲線算法中的最基本運(yùn)算，本文對(duì)[Koe96]中的橢圓曲線標(biāo)量乘法作了改進(jìn)av网站啊啊啊啊，提高了其運(yùn)算速度在线看片无码永久免费A；橢圓曲線的參數(shù)的選擇直接影向到橢圓曲線密碼體的安全性，文中利用復(fù)乘方法構(gòu)造了具有良好密碼特性的橢圓曲線欧美AAA性爱网站，并實(shí)現(xiàn)了橢圓曲線上ElGamal公鑰體制性欧美国产片；文中還給出了利用Goldwasser-Kilian定理和橢圓曲線的復(fù)乘方法進(jìn)行素?cái)?shù)的確定判別算法；最后討論了利用橢圓曲線分解整數(shù)的方法并進(jìn)行了某些改進(jìn)欧美日韩国产亚欧在线观看，在PC機(jī)上分解了兩個(gè)28位素?cái)?shù)之積的55位整數(shù)激情视频小说理论。

By using unified method , we investigate decomposability of real or complex cubic polynomials in several elements .

這里欧美特一级AAAAA禁片，本文將運(yùn)用統(tǒng)一的方法對(duì)實(shí)數(shù)域和復(fù)數(shù)域上的多元三次多項(xiàng)式的分解問題加以討論国产一级特级黄色网站。

Bull; Decomposability: if some work has already been done to analyze the modular structure of the problem domain, it may provide a good starting point for the modular decomposition of the software.

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From 1920s up to Now, various techniques and methods for wave field decomposition, propagation and migration/imaging have been well developed, such as the Kirchhoff asymptotic method, frequency-wavenumber domain phase-shift and phase-shift-plus-interpolation methods, and the one-way wave equation based phase-screen and generalized screen methods, etc.

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It includes the basic structural theory of groups; groups'actions on sets and the applications of these actions; the basic structures of rings; the properties of uniquely factorized domains; the Chinese Remainder; the extensions of fields; finite fields with applications; the Galois theory with applications.

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Tansformed the real part and imaginary part of interferogram to stationary wavelet domain, analyzed the PDF of signal and noise wavelet coefficients using Pearson distribution system, then evaluated the wavelet coefficients of signal in stationary wavelet domain by Maximum A Posterior criteria to reconstruct the interferogram.

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In three cases, we investigate the decomposition of a polynomial f=x~n -u in a local field to factor a prime ideal of K in its extension.

在這三種情況下，我們研究多項(xiàng)式f=x~n－u局部域上分解情況95精品视频，得出相應(yīng)K上素理想具體分解形式欧美精品观看视频免费。

In the following two cases:(1)gcd=1;(2) N=p〓, where p denotes the characteristic of the finite field GF, by using the factorization of the polynomial in finite field, the counting function N〓 is showed, the expected value of the linear complexity E〓 is determined, and a useful lower bound on the expected value of the k-error linear complexity E〓 is established.(7) The stability of the lattice structure for pseudorandom number sequences is put forward.

利用多項(xiàng)式的因式分解等簡單工具，研究了任意有限域GF上日日干日日射日日操，周期N與p互素以及N ＝P〓這兩種情況下樱桃视频iosapp，計(jì)數(shù)函數(shù)N〓，的值经典在线视频日韩精品免费播放，即線性復(fù)雜皮為c的N-周期序列的個(gè)數(shù)91国在线视屏，并給出了線性復(fù)雜度的數(shù)學(xué)期望E〓的值以及k-錯(cuò)線性復(fù)雜度的數(shù)學(xué)期望E〓的一個(gè)有用的下界，這里p表示有限域GF的特征日韩国产欧美免午夜网。

In the following two cases:(1)gcd = 1 ;(2)N = p~v, where p denotes thecharacteristic of the finite field GF, by using the factorization of the polynomialin finite field, the counting function N_(N,0) is showed, the expected value of thelinear complexity E_(N,0) is determined, and a useful lower bound on the expectedvalue of the k-error linear complexity E_ is established.(7) The stability of the lattice structure for pseudorandom number sequences is putforward.

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Aerial image can be computed fairly fast by this method compared with the rigorous solution of the Hopkins equation, especially for the situation of many sparse aerial points which is often met in OPC application.

一個(gè)雙線性光學(xué)系統(tǒng)分解成為一組空間域卷積核强奷年轻貌美女教师在线观看，并通過對(duì)版圖的空間域卷積來計(jì)算空間光強(qiáng)。與采用Hopkins公式的SPLAT相比福利精品在线，這種方法能快速地計(jì)算空間光強(qiáng)就去干黄色激情图片小说。尤其對(duì)于大面積計(jì)算顯得更為有效。