normal polynomial 中文意思是什麼

normal polynomial 解釋
正規多項式
  • normal : adj 1 正常的，平常的，普通的；平均的。2 正規的，標準的，額定的，規定的。3 智力正常的，精神健全的...
  • polynomial : adj. 1. 【動、植】多詞學名的。2. 【數學】多項式的。n. 1. 【動、植】多詞學名。 2. 【數學】多項式。
  1. Firstly, we generalize and analyze the advantages and present research of elliptic curve cryptography ; secondly, we study the basic theory of the ecc ; thirdly, we illustrate the safety of the ecc and discuss the elliptic curve key agreement scheme, elliptic curve encryption scheme and elliptic curve digital signature algorithm ; fourthly, we study fast algorithms of the multiplication and inversion multiplication of the element of in the underlying finite field f2m whose characteristic is two represented by the two basis of optimal normal basis and polynomial basis. we make improvements to the fast algorithm of the polynomial basis multiplication by hankerson and base on the experiments, we describe the properties and compare the advantages of the multiplication and inversion multiplication of the elements in f2m field under optimal normal bases and polynomial basis. results concluding from the study car be used as references in the realization of the elliptic curve cryptosystem ; fifthly, we overview the current fast algorithm of point multiplication, improve the fix base point comb algorithm, advance the speed of the whole system and remark the advantages and disadvantages of the popular algorithms based upon the experimental datas ; sixthly we realize the algorithm library of elliptic curve cryptography based on the f2m. only change slightly in our algorithm library can we realize the ecdh, eces, ecdsa based onf2m of anysize ; seventhly, we realize the ecc on two secure elliptic curves, including ecdh, eces, ecdsa

    本文首先介紹並分析了橢圓曲線密碼體制的優點及研究現狀；其次研究了橢圓曲線密碼體制的基本理論；第三，分析了橢圓曲線密碼的安全性並介紹了密鑰共享，加密，數字簽名等橢圓曲線密碼體制；第四，深入研究了特徵為2的有限域f _ 2m中的元素在多項式基和最優正規基表示下的乘法運算和乘法逆運算的快速演算法，並對hankerson等人提出的多項式基下的乘法運算的快速演算法作了改進，而且在實驗的基礎上不僅分析研究了f _ 2m域中元素在多項式基和最優正規基表示下的乘法和乘法逆運算的性能，還對這兩種基表示下的f _ 2m域中元素運算效率的優劣作了比較和研究，所得的結論可供在實現橢圓曲線密碼體制時參考；第五，研究了目前流行的計算橢圓曲線標量乘法的快速演算法，同時改進了固定基點梳形法，提高了整個系統的速度，並在實驗的基礎上分析研究了流行演算法的優劣；第六，實現了基於f _ 2m的橢圓曲線密碼體制的演算法庫，在我們的演算法庫中只需稍微改變便能實現基於任意尺寸的f _ 2m上的ecdh ， eces ， ecdsa等橢圓曲線密碼體制；第七，實現了兩條安全橢圓曲線上的橢圓曲線密碼體制，包括ecdh ， eces ， ecdsa 。
  2. The parametric speed of the curve is firstly approximated by the bezier polynomial which takes the lengths of control polygon ' s edges of the direction curve of normal as bezier coordinates. then the corresponding geometric offset approximation algorithm is given. moreover, an offset approximation with high precision is obtained by degree elevation of the direction curve of normal

    首先利用以法矢方向曲線的控制多邊形邊長為b zier縱標的b zier多項式來逼近曲線的參數速度，給出了相應的幾何等距逼近演算法，進一步結合法矢方向曲線的升階獲得了高精度逼近
  3. One is the 191 bits secure curve of ansi x9. 62, elements in f2m field represented by polynomial basis, the other is the 148bits secure curve in our secure curve library elements in f2m field represented by optimal normal basis ; the conclusion summarizes the whole paper and preview the the further developments of the work we have done

    一條是ansix9 . 62中的191bit的安全曲線， f _ 2m中的元素用多項式基表示，一條是我們安全曲線庫中的148bit的安全曲線， f _ 2m中的元素用最優正規基表示；最後對本文進行總結和展望了以後的工作。
  4. Then the unified approach can be applied to it to acquire the ensemble random evolutionary response. since the normal probability density function ( pdf ) may lead to instability of some sample systems when the random parameters taking sufficiently small negative values, an arch - like pdf and a more adaptable - pdf, together with the matching chebyshev polynomial approximation and gegenbauer polynomial approximation, are suggested. numerical examples show that the suggested methods are effective

    相比較而言，隨機模擬法的結果無疑是最可靠的，但是它的計算量嫌大；隨機攝動法的計算量遠小於隨機模擬法，但是它要求隨機攝動量必須是一個小量；正交展開法的計算精度好於隨機攝動法，其得到結果與隨機模擬法得到的結果幾乎吻合，其計算量略多於隨機攝動法，但與隨機模擬法相比要少的多，不過計算前的準備工作較費時。
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