Abstract: A universal Galois field multiplier which is adaptable to any form of polynomial having a predetermined n-order when it is controlled by a coefficient of polynomial which defines a Galois field, which includes second AND-gates each for ANDing a corresponding bit value of the multiplicand and one bit value among the remaining bits of the multiplier; first XOR-gates each for XORing a corresponding leftwardly rotated output value of the second AND-gates and a corresponding output value of the preceding operation unit; third AND-gates each for ANDing the corresponding coefficient value of the generating polynomial and a most significant bit value among the output values of the preceding operation unit; and second XOR-gates for XORing output values of the third AND-gates and the first XOR-gates, wherein the second XOR-gates become effective in accordance with outputs of the third AND-gates.