A Study on the Construction of the perallel Multiplier over Galois Field

초록

The multiplication algorithm using the primitive irreducible trinomial x^m+x+1 over GF(2^m) was proposed by Mastrovito. The multiplier proposed in this paper consisted of the multiplicative operation unit, the primitive irreducible operation unit and modular operation unit. Among three units mentioned above, the primitive irreducible operation was modified to primitive irreducible trinomial xm+xn+1 that satisfies the range of 1<n<m/2. The multiplicative operation unit was adopted from an existing algorithm. The results of the primitive irreducible operation unit and the multiplicative operation unit were used for computing the mod operation unit. The primitive irreducible polynomial would be better if the size of the result of multiplication operation unit in the process of converting x^m,…,x^2m-2 to x^m-1,…,x^0 is reduced. In this paper, the primitive irreducible polynomial was reduced to the primitive irreducible trinomial proposed. As a result of this reduction, the primitive irreducible trinomial reduced the size of circuit. In addition, the proposed design of multiplier was suitable for VLSI implementation because the circuit became regular and modular in structure, and required simple control signal.