Abstract: Polynomial modulo reduction algorithms are one of the fundamental issues of computer algebra,and widely used in coding algorithms and cryptographic system design.Two basic reduction operators,namely word reduction operator and semi-word reduction operator,are presented.Furthermore,it is proved that the computation time of the two operators are invariant if some conditions hold,and the computation time of the modulo reduction algorithms are of linear form.These can be the theoretical foundation for the algorithm design and analysis.Moreover,the two operators are applied to AES and ECC algorithms in some examples.