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