模归约算法表达式自动生成算法设计与实现

J4 ›› 2013, Vol. 12 ›› Issue (4): 12-16.

模归约算法表达式自动生成算法设计与实现

1.大理学院数学与计算机学院，云南大理 671003；2.云南大学数学系，昆明 650091

收稿日期:2012-09-07 出版日期:2013-04-15 发布日期:2013-04-15
作者简介:杨邓奇，讲师，博士，主要从事网络安全、密码学和网络体系结构研究.
基金资助:
云南省自然科学基金资助项目（2010ZC142）

The Design and Implement of Algorithm Expression Auto-generation for Modulo Reduction Operation

1.College of Mathematics and Computer, Dali University, Dali, Yunnan 671003, China；
2.Department of Mathematics, Yunnan University, Kunming 650091, China

Received:2012-09-07 Online:2013-04-15 Published:2013-04-15

摘要/Abstract

摘要：

多项式模归约算法是计算机代数中的基本问题之一，在编码算法和密码体制设计中有着广泛应用。基于对模归约数学
基础的分析，设计了模归约算法表达式自动生成算法，只要选择实现所需的字宽w和模多项式M（x）的系数，即可自动生成对应的模规约算法表达式，为模规约算法在密码编码学中的应用提供了基础。

关键词: 模归约算法, 计算代数, 算法表达式自动生成

Abstract:

Polynomial modulo reduction operation is one of the fundamental issues of computer algebra, and widely used in coding algorithms and cryptographic system design. Based on the analysis on the mathematic foundation of modulo reduction operation, this paper designs the expression auto-generation algorithm of modulo reduction operation. This algorithm can auto-generate the algorithm expression of modulo reduction operation according to the selected word-width and modulo polynomial. This provides a foundation for the application of modulo reduction algorithm in the areas of cryptography and encode, such as ECC, AES and CL-PKC.

Key words: modulo reduction algorithms, computer algebra, algorithm expression auto-generation

中图分类号:

O157
TP301.6

杨邓奇, 陆正福, 左国超. 模归约算法表达式自动生成算法设计与实现[J]. J4, 2013, 12(4): 12-16.

YANG Deng-Qi, LU Zheng-Fu, ZUO Guo-Chao. The Design and Implement of Algorithm Expression Auto-generation for Modulo Reduction Operation[J]. J4, 2013, 12(4): 12-16.