Parallel GF(3m)GF(3m) multiplier for trinomials

In this paper, we propose a parallel multiplier over arbitrary finite field GF(pm)GF(pm). In particular, we apply the proposed multiplier to GF(3m)GF(3m) defined by irreducible trinomial which has received a great interest recently. The proposed GF(3m)GF(3m) multiplier is not only the first parallel multiplier with explicit complexities, but its complexities also match with generalized forms of the complexities of the most efficient GF(2m)GF(2m) multiplier.

► We propose a parallel multiplier over arbitrary finite field GF(pm)GF(pm).
► We present a parallel GF(3m)GF(3m) multiplier for irreducible trinomial.
► We give explicit complexities for the proposed parallel GF(3m)GF(3m) multiplier for the first time.