正规基 meaning in Chinese
normal basis
Examples
- On normal basis of field extension
关于域扩张上的正规基 - An algorithm on the multiplication table of the normal basis over finite fields
关于有限域上正规基乘法表的一个算法 - 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
一条是ansix9 . 62中的191bit的安全曲线， f _ 2m中的元素用多项式基表示，一条是我们安全曲线库中的148bit的安全曲线， f _ 2m中的元素用最优正规基表示；最后对本文进行总结和展望了以后的工作。 - 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
本文首先介绍并分析了椭圆曲线密码体制的优点及研究现状；其次研究了椭圆曲线密码体制的基本理论；第三，分析了椭圆曲线密码的安全性并介绍了密钥共享，加密，数字签名等椭圆曲线密码体制；第四，深入研究了特征为2的有限域f _ 2m中的元素在多项式基和最优正规基表示下的乘法运算和乘法逆运算的快速算法，并对hankerson等人提出的多项式基下的乘法运算的快速算法作了改进，而且在实验的基础上不仅分析研究了f _ 2m域中元素在多项式基和最优正规基表示下的乘法和乘法逆运算的性能，还对这两种基表示下的f _ 2m域中元素运算效率的优劣作了比较和研究，所得的结论可供在实现椭圆曲线密码体制时参考；第五，研究了目前流行的计算椭圆曲线标量乘法的快速算法，同时改进了固定基点梳形法，提高了整个系统的速度，并在实验的基础上分析研究了流行算法的优劣；第六，实现了基于f _ 2m的椭圆曲线密码体制的算法库，在我们的算法库中只需稍微改变便能实现基于任意尺寸的f _ 2m上的ecdh ， eces ， ecdsa等椭圆曲线密码体制；第七，实现了两条安全椭圆曲线上的椭圆曲线密码体制，包括ecdh ， eces ， ecdsa 。