multiplier factor exclusive or gates xor11 to xor14 each for rotating left an output of each corresponding one of the exclusive or gates xor6 xor10 xor8 and xor9 and adding a value resulted from the left rotation to an output of each corresponding one of the and gates ad13 to ad16 and an exclusive or gate xor15 for adding an output of the exclusive or gate xor9 arranged in one of the remaining items to an output of the exclusive or gate xor12 now the galois field multiplication method of the present invention and the multiplier embodied in accordance with the method will be described in detail although the above two operation methods examples 1 and 2 are basically identical to each other only the former method of example 1 is used in the general four arithmetical operations because the addition of the general four arithmetical operations involves a carry in an addition for galois field however a phenomenon where the degree of the highest item of a generated polynomial g x is decreased occurs because the addition involves no carry thereby establishing a condition of g x 0 for example in a case of g x x 4 x 1 34 x 4 34 is equal to 34 x 1 34 x 4 x 1 in other words 34 x 4 34 is substituted by 34 x 1 34 therefore for the multiplication for.