Efficient Bit-Parallel Shifted Polynomial Basis Multipliers for All Irreducible Trinomial

Finite Field multiplication operation is one of the most important operations in the finite field arithmetic. Recently, Fan and Dai introduced a Shifted Polynomial Basis(SPB) and construct a non-pipeline bit-parallel multiplier for . In this paper, we propose a new bit-parallel shifted polynomial basis type I and type II multipliers for defined by an irreducible trinomial . The proposed type I multiplier has more efficient the space and time complexity than the previous ones. And, proposed type II multiplier have a smaller space complexity than all previously SPB multiplier(include our type I multiplier). However, the time complexity of proposed type II is increased by 1 XOR time-delay in the worst case.