剩余定理

It includes the basic structural theory of groups; groups'actions on sets and the applications of these actions; the basic structures of rings; the properties of uniquely factorized domains; the Chinese Remainder; the extensions of fields; finite fields with applications; the Galois theory with applications.

主要内容包括群的基本结构理论、群在集合上的作用及其应用、环的基本结构和因子分解理论、中国剩余定理、域的扩张理论、有限域及其应用、Galois 理论及其应用。

The author mainly realized the method of generating the large random numbers and judging the prime number using Lehmann means,then three pairs of secure key with different lengths (256 bits,512 bits,1024 bits) was generated to meet the demand of different security grade. In encryption module,modular multiplication arithmetic of large number was realized adopting addition chaining. In decryption module,extended Euclid was used to get inverse,and the Chinese remainder theorem was used to realize decryption,which increased the speed of decryption greatly.

作者主要实现了大随机数的生成、采用整除小素数和勒曼测试法判定素数，可以生成三种不同长度的密钥对(256位、512位、1024位)来满足不同的加密安全等级的需求；加密模块中，选用了二进制序列的乘法方法，实现了大数模幂乘运算；解密模块中，引用了扩展的欧几里德法求逆元，并采用中国剩余定理实现解密过程，大大提高了解密速度。

In this algorithm, the product of two huge primes is the secret information, which is further converted into n natural numbers and then encoded into planted plane cubic tree structures which are embedded into the software codes as software watermark.

水印嵌入的入程是：首先将两个大质数的乘积采取中国剩余定理划分成n个天然数，然后再将这n个天然数编码入n个平面环路树PPCT构造中，将这些构造的构建代码嵌入软件代码中。

Debugging software is needed in the recognizing phase, it is used to watch the execution state, when all planted plane cubic tree structures are detected, they will be decoded into n natural numbers, and the original product of two prime numbers will be got through Chinese Remaining Theory.

水印的检测可以通过调试软件来实现，让调试软件监督嵌入水印的受维护程序的执行，当检测到全体n个PPCT构造后，将它们全体解码为n个天然数，最后应用中国剩余定理将这n个天然数还原出最初的两个大质数的乘积亦即最初的水印信息。

A good use of the integer type, the biggest 9999990 to support the decimal integer, It can perform large integers, plus or minus, multiplication, addition and modular, with a big round of the largest factions, extended Euclidean algorithm, the Chinese remainder theorem algorithm, Miller - Rabin primality testing algorithm, random generation of arbitrary integer spaces such as libraries, This kind of dynamic library has been used for commercial software, the reliability and speed is affirmed.

一个很好用的大整数的类，最大可支持9999990位的十进制整数，可进行大整数的加、减、乘、除和取模运算，并带有求大整数的最大公因数、扩展Euclidean算法、中国剩余定理算法、Miller-Rabin素性测试算法、随机生成任意位的大整数等函数库，这个类的动态库曾用于商业软件之中，其可靠性和速度是得到确认的。

O To describe the Chinese remainder theorem and its application.

o讨论中国剩余定理及其应用。

Classic Chinese Remainder Theorem solving program, you have to import the solution congruence theorems can be solved by!

经典的中国剩余定理求解程序，输入你所要解的同余式即可按定理求解！

This paper proposed a directed threshold signature scheme based on the Chinese Remainder Theorem and Schnorr's signature scheme.

文章运用中国剩余定理，提出了基于中国剩余定理、ELGamal公钥密码理论和Schnorr理论的有向门限签名方案。

Of course, the major reason for this is that the basic algorithms are very complex (such as Chinese Remainder Theorem, Theory of Quadratic Residues, and many kinds of cryptagraphic algorithms).

当然造成这种结果的原因是因为实现这些方案的基础算法很复杂（例如中国剩余定理、平方剩余定理以及各种密码算法）。

This theorem calls " of " China residue theorem, also call " grandchildren theorem " or " big develop begs one art ".

这个定理就称为"中国剩余定理"，也叫"孙子定理"或"大衍求一术"。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷