| 1. | The " key usage " extension field specifies the usage of the key pair
"密码匙用途"的扩充字段规定一对密码匙的用途。 |
| 2. | Cyclic extension field
循环扩张域 |
| 3. | Application of irreducible decomposition of polynomials over algebraic extension fields in cryptography
代数扩张域上的多项式分解在密码学中的应用 |
| 4. | Although the computation of order e ( gf ( pm ) ) for elliptic curve finite field is a very difficult problem , the case in optimal extension fields ( oef ) is relatively easy
针对本文所使用的最优扩域oef ，椭圆曲线有限群阶。你计d的计算比较容易，本文利用血mc 。 |
| 5. | The techniques for constructing extension fields are typically more involved than those for constructing prime fields and draw largely from the theory of polynomials over finite fields
构造扩展域的技术比那些构造素数域的要复杂的多，而且大多数是建立在基于有限域的多项式理论基础上的。 |
| 6. | But this reduction is not applicable to optimal extension fields ( oef ) . in order to solve this difficult problem , a " quadratic residue algorithm of double - modulep , p ( x ) " is presented
为了解决这一问题，本文推广并证明了“重模p ， p铜的二次剩余算法” ，从而使得这一步骤得到完善。 |
| 7. | This thesis is divided into two parts . the first one is the research on the feature of composition fields and optimal extension fields as well as the fast algorithm in those fields . the other one is the implementation of those improved algorithms
研究工作分为两个部分,一部分是对复合域、理想扩域的结构特点和其上的快速运算算法的分析、研究；另一部分是对这些快速算法的测试改进，即本地实现。 |
| 8. | The main contributions of the dissertation are summarized as follows . ( 1 ) elliptic curve cryptosystems in optimal extension fields ( oef ) , including elgamal encryption algorithm , diffie - hellman key agreement scheme and elliptic curve digital signature algorithm ( ecdsa ) , are implemented , and a software package , which is applicable to microcomputers , is developed
本文所取得的主要研究成果是： ( 1 )完整实现最优扩域oef上的椭圆曲线密码体制，其中包括elgamal加密算法、 diffie - hellman密钥共享方案以及椭圆曲线数字签名算法ecdsa ，并且提供了相应的适合在微机上实现的软件包。 |
