Methods for computing the CRC of a message from the incremental CRCs of composite sub-messages

A method for adjusting an m-bit CRC of a sub-message, wherein the sub-message corresponds to a composite sub-message having n trailing zeroes, where m and n are integers, comprising:

• storing the m-bit CRC in an m-bit memory location;
• examining each bit of N, where N is a binary representation of a result of n mod (2m−1), in order from a most significant bit to a least significant bit;
• the examining act for each examined bit comprising:
• finite field squaring the contents of the m-bit memory location, and;
• if the examined bit equals one, advancing the contents of the m-bit memory location to a next state as determined by a Galois field defined by a CRC generating polynomial for generating the m-bit CRC.

A method of advancing an m-bit sequence through n states of a Galois field generated by a primitive or irreducible polynomial of degree m, where m and n are integers, comprising:

• storing the m-bit sequence in an m-bit memory location;
• examining each bit of N, where N is a binary representation of a result of n mod (2m−1), in order from a most significant bit to a least significant bit;
• the examining act for each examined bit comprising:
• finite field squaring the contents of the m-bit memory location, and;
• if the examined bit equals one, advancing the contents of the m-bit memory location to a next state as determined by the Galois field.