Also we study the ecc crypto theory in the field of public crypto system , in which the ecc encrypt principle , safety , reliability , as well as the structure of ecc based on galois field is focused on 研究了公钥加密系统中的椭圆曲线加密理论，详细阐述了有限域上椭圆曲线的结构及其基本运算； 3
The calculation speed over finite fields greatly affects the performance of ecc implementation . so , to find a fast algorithm for finite field calculation becomes a hot field in recent cryptography researches Ecc中有限域上运算的速度极大地影响ecc实现速度，寻找有限域快速运算算法也就成了近年来密码学研究的一个热点领域。
Chapter 3 introduces the correcting ability of the rs code . then it particularly states the definition and algorithm of galois field , and analyses the realization of the limited field multiplier based on the dual basis 第三章分析讨论了rs码的特点,给出了伽罗华有限域的定义与运算规则,推导和分析了基于对偶基的有限域乘法器实现方法。
Elliptic curve cryptosystem is one of the most important , cryptosystems , which is obtained by substituting finite group of elliptic curve on finite field for finite group of cryptosystem based on discrete logarithm problem 椭圆曲线密码体制是用有限域上的椭圆曲线有限群，代替基于离散对数问题密码体制中的有限群所得到的一类密码体制。
Polynomials over the finite field include cyclotomic polynomials and irreducible polynomials constructed on different theories . in this paper , their properties and ways for their construction are explored and discussed 摘要有限域上的多项式有分圆多项式和不可约多项式，其中各由数条原理构成。文中对其性质和构造方法进行了具体研究与论述。
First , considering the construction characteristic of reed - solomon code , we present a kind of new construction method for linear codes by using the factorization properties of cyclotomic polynomials on finite fields 在纠错码的设计与分析方面：首先，结合reed - solomon码的构造特点，利用有限域f _ q上分圆多项式的分解特性来构造f _ q上线性码。
In section 3 , we get an algorithm to look for a primitive root of fp ~ ( 2 ) from a given primitive root of the finite field fp . what ' s more , a table of primitive roots over fp ~ ( 2 ) can be provided for those prime numbers p ( p < 200 ) 第三节中，我们从有限域fp的原根出发得到了一个求fp ~ 2的原根的算法，而且对较小的p ( p 200 )得到fp ~ 2的原根表。
By initiating the values of vector description for a primitive element , all finite field elements could be generated by continue cyclic shifting , gmw sequences then could be generated by trace function calculation 通过预置本原元向量表达的初始值，不断的进行向量循环移位来生成有限域中的元素。生成有限域中所有元素后，即可按迹函数计算出gmw序列。
Proceed from general conclusion of algebra on the finite field , study this special algebra system of elliptic curve on the finite field , discuss that sets up several theories of the public key cryptosystems and the problems of implementation on it 从有限域上的代数的一般结论出发，研究有限域上的椭圆曲线这一特殊的代数系统，讨论在其上建立公钥密码体制的若干理论和实现问题。
In resent years , the theory of ring of coding and cryptography is the key for researcher in coding and cryptography . in particular , the study of code over z4 . in this paper , the main results are the following : 1 近年来，很从事编码密码理论的研究者将研究的兴趣从有限域上的编码密码理论转移到有限环上，尤其是z _ 1码的研究，通过gray映射，将z _ 1上的码与域上二元码联系起来。
