A Study on Constructing the Arithmetic Unit over GF(3m)

In this paper, we presented a method of constructing a multiplier over finite field GF(3
^m
). We proposed the multiplication and mod F(X) arithmetics at the same time. The proposed multiplier is composed as following parts. There are multiplication part, data assortment part, P
_j
term accumulation and sequential selection part, descending order mod F(X) generation part and multiplication processing part. Especially, the proposed multiplier have regularity, expansibility and modularity of circuit design.