模归约算法表达式自动生成算法设计与实现

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

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。

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.