Very Fast and Economical GF(2^8) Divider Circuit Based On GF(2^2) Field Operation

Abstract

This paper describes how to design a Galois field GF(2 8 )dividing circuit using double subfield transformation[5]. The circuit is much faster and more efficient than the classical GF(2 8 ) divider . Multiplier circuit is used mainly for ECC encoding and for the Encripting machine while the Divider is used for ECC decoding and the Decripting machine. The divider in the paper is designed based on the GF(2 2 ) inversing circuit and we applied double subfield transformation. We compared the new design with the classical design in both respects, speed and cost so find the new design is much better than the classical design.