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In this paper, we present a bit-parallel multiplier for GF(2m) defined by an irreducible pentanomial ixm + xk3 + xk2 + xk1 + 1, where 1 ≤ k1 < k2 < k3 ≤ m/2. In order to design an efficient bit-parallel multiplier, we introduce a shifted polynomial basis and modify a reduction matrix presented by Reyhani-Masoleh and Hasan. As a result, the time complexity of the proposed multiplier is TA + (3 + [log2(m - 1)])Tx, where TA and Tx are the delay of one AND and one XOR gate, respectively. This result matches or outperforms the previously known results. On the other hand, the proposed multiplier has the same space complexity as the previously known multipliers except for special types of irreducible pentanomials. Note that its hardware architecture is similar to that presented by Reyhani-Masoleh and Hasan. [ABSTRACT FROM AUTHOR]

Applying the matrix-vector product idea of the Mastrovito multiplier to the GF(2m) Montgomery multiplication algorithm, we present a new parallel multiplier for irreducible trinomiats. This multiplier and the corresponding shifted polynomial basis (SPB) multiplier have the same circuit structure for the same set of parameters. Furthermore, by establishing isomorphisms between the Montgomery and the SPB constructions of GF(2m), we show that the Montgomery algorithm can be used to perform the SPB multiplication without any changes and vice versa. [ABSTRACT FROM AUTHOR]