Abstract: This paper puts forward a modified two-table method and a directly table-searching method to accomplish the algebraic arithmetic on the Galois Field based on the arithmetical principle. The new two-table method consumedly decreases the total number of table-searching and predigests the algorithm for error controlling system. The merit of the improved two-able method is expounded through the quantitative analysis of the arithmetic and calculation quantity. At last,this paper quantificationally compares the directly table-searching method and the two-table method.