A Study on the Design of Highly Parallel Multiplier using VCG over GF(3m)

초록

This note describes a new designed multiplier using VCG that computes the product of two arbitrary elements of the Galois Field GF(3m). Firstly, we provide the Vector Code Generator (VCG) circuit that generate each vector codes of element α(i), …, α(i+1) over GF(3m). Using the VCG, we can get all vector codes necessary for multiplication over GF(3m). Secondly, using these vector codes, we design multiplication circuit for any two elements in GF(3m). For the proposed circuit in this paper, we show the example in GF(33) and circuit design.