大整数算术的实现

大整数算术的实现(论文8500字,程序清单)
摘要：密码学在信息安全领域起着基本的、无可替代的作用[1]。RSA algorithm、驾驶安全预警与导航系统、错误检查和纠正等公钥密码算法还有数字签名都是在大整数运算的基础上在才得以实现并快速发展的。由于这些公钥密码算法频频使用大整数算法中的四则运算及其它基础算法，所以如果可以提升这些基础算法的运算速度，就可以有效地解决上述公钥密码算法耗时的难题。因此大整数运算的实现与开发是本文研究的重点。
本程序是在windows 32位系统上完成的。首先先建立大整数运算程序的基础框架并当部分辅助函数已经成功实现后，再将新完成的部分程序加进去。这种模块化的思想使得每当完成一部分程序后，都可以将它加入大整数运算程序基础框架中然后立马见到成效和错误，方便自己的改正和优化，这样就避免了直到整体完成后才发现不明原因错误的烦恼。Microsoft Visual C++6.0是本程序完成制作并进行调试的主要操作工具，在程序中力求达到足够高效率的基本运算[2]。其次为了使本程序具备可移植性和稳定性，创建了简单明了的函数接口。清晰易懂的代码，友好的用户界面和对于异常的表达式会提示出错，这些同样都是本程序所要完成的。
关键词：超大整数；代码清晰易懂；模块化思想；高精度；
 
The realization of large integer arithmetic
Abstract：Cryptography plays a fundamental and irreplaceable role in the field of information security. RSA algorithm, driving safety early warning and navigation system, error checking and correcting the public key cipher algorithm and digital signature is on the basis of large integer arithmetic to implement and fast development. Due to the frequently used public key cryptography algorithm algorithm of big integer arithmetic and other basic algorithm, so if based algorithm can improve the computing speed, can effectively solve the problem of the public key cipher algorithm takes. Therefore, the implementation and development of large integer operations is the focus of this paper.
This procedure is done on Windows 32 bit system. The basis of the first to establish a large integer arithmetic program frame and when part of the auxiliary function has been successfully implemented, then added new complete part of the program. The modular thought makes every time after completion of part of the program can be to add it to the big integer arithmetic program based framework and then immediately see results and errors, convenient your correction and optimization, thus avoiding the unexplained mistake until after the found trouble. Microsoft Visual c + + 6.0 is made of the completion of this program and debug the main operating tools, enough to achieve high efficiency in application of the basic computing. Secondly in order to make this program has the portability and stability, to create a simple function interface. Transparent code, friendly user interface and for abnormal expression will prompt wrong, these also are to complete the program.
Key words：Large integer; The code clear and easy to understand; Modular thinking; High precision;
 

目 录
中文摘要    3
英文摘要    4
第一章绪论    5
1.1研究背景和意义    5
1.1.1 研究背景    5
1.1.2研究意义    5
1.2国内外研究现状    6
1.3本文的研究内容    6
第二章用户界面    7
2.1用户界面流程图    7
2.2用户界面截图    7
第三章数据结构    8
3.1数据结构的处理    8
3.2符号    8
3.3函数    9
第四章算法    9
4.1大整数加法运算    9
4.1.1算法介绍    9
4.1.2加法运算程序的解读    9
4.1.3加法运算程序的流程图    10
4.1.4加法运算程序的截图    11
4.2大整数减法运算    11
4.2.1算法介绍    11
4.2.2减法运算程序的解读    11
4.2.3减法运算程序的流程图    12
4.2.4减法运算程序的截图    13
4.3大整数乘法运算    13
4.3.1算法介绍    13
4.3.2乘法运算程序的解读    13
4.3.3乘法运算程序的流程图    14
4.3.4乘法运算程序的截图    15
4.4大整数除法运算    15
4.4.1算法介绍    15
4.4.2除法运算程序的解读    15
4.4.3除法运算程序的流程图    16
4.4.4除法运算程序的截图    16
第五章总结与展望    17
参考文献    18
致谢    19