互余关系在密码学中应用及相关性质推广

Application of Complementary Relation in Cryptography and Its Correlated Property Populariziation

互余关系是基础数论中一个重要的理论概念。文中介绍了互余关系在典型椭圆曲线密码（EGG）方程中的简单应用，并根据互余关系和相关性质，进一步给出了互余关系中孙子互余定理一些等价转换定理的若干推论，以及模mi非互素情形的解法和相互关系。这些结果扩充了互余关系的基本理论，而且在密码学中有着实际的应用。

Complementary Relation is an important theoretic conception in basic mathematics theory. In this paper, the simple application of Complementary Relation in typical Elliptic curve Cryptography （ECC） is described. Based on complementary Relation and correlated property, two inferences for a conversion theorem of equal values in Chinese Complementation Remainder Theorem, the general algorithm for the modulus m, of Non-Pairwise Relatively Prime and some relation are given. These result has expanded basic theory of complementary relation, and the practical application is found in cryptography.