橢圓四次曲線 的英文怎麼說
中文拼音 [tuǒyuánsìcìqūxiàn]
橢圓四次曲線
英文
elliptic quartic curve- 橢 : Ⅰ形容詞（卵形） oval-shapedⅡ名詞[書面語] （長圓形的容器） elliptic vessel
- 四 : Ⅰ數詞（三加一后所得） four Ⅱ名詞1 [音樂] （中國民族音樂音階上的一級） a note of the scale in gong...
- 次 : Ⅰ名詞1 （次序; 等第） order; sequence 2 [書面語] （出外遠行時停留的處所） stopping place on a jou...
- 曲 : 曲名詞1 （一種韻文形式） qu a type of verse for singing which emerged in the southern song and ji...
- 線 : 名詞1 （用絲、棉、金屬等製成的細長的東西） thread; string; wire 2 [數學] （一個點任意移動所構成的...
- 橢圓 : [數學] oval; oval shaped; ellipse; ellipsoid橢圓規 ellipsograph; [圖] elliptic trammel; 橢圓軌道 ...
- 曲線 : [數學] curve; bight; bought; profile; net曲線板 french curve; irregular curve; curve board; splin...
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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 。The procedure of this dissertation divides into two hierarchies. first, the finite field gf ( pm ) and arithmetic among field elements are concerned in chapter 3 and chapter 4. second, elliptic curve finite group e ( gf ( pm ) ) and arithmetic among point elements are concerned in chapter 5 and chapter 6
本文的工作可分為兩個層次：第一層次，關于基域gf （ p ~ m ）及其域元素之間的運算，這包括在第三和第四章；第二層次，關于橢圓曲線有限群e （ gf （ p ~ m ） ）及其點元素之間的運算，這包括在第五和第六章。
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