2 4 2 8 A Serial Multiplier over the Subfields GF2^8 of Galois field GF2^4

摘要

PURPOSE: A design for a GF(2¬8) serial multiplier using a GF(2¬4) infinite field is provided to reduce delay time to get result, and to realize the serial multiplier with hardwares less than a parallel multiplier by designing the serial multiplier of the GF(2¬8) finite field with the use of a serial operator on a subfield. CONSTITUTION: In case that an order of the GF(2¬m) is consisted of the multiplication of two numbers larger than one, the GF(2¬m) has the subfields of GF(2¬u) and GF(2¬v). The serial multiplier on the GF(2¬m) finite field is realized by using the serial operators on the subfields. Thus, the serial multiplier is realized by 16 2-input AND gates and 15 2-input XOR gates.