A cyclic redundancy check (CRC) generator, in accordance with a specific embodiment of the present invention, generates a 32-bit CRC for each packet whose data bytes are carried over a 128-bit bus by first dividing the data bytes by a 123.sup.nd degree generator polynomial and subsequently dividing the remainder of the first division by a 32.sup.nd degree generator polynomial. Data bytes of a new packet are divided by a different dividing logic than those of a current packet. The remainder of division performed on the bytes of a new packet are supplied to the dividing logic adapted to divide the bytes of a current packet. The division by the 123.sup.nd degree generator polynomial is performed on a per byte basis, with the remainder of the division of the (i+1).sup.th byte being used in the division of the i.sup.th byte.