Fast Bit-Parallel Shifted Polynomial Basis Multiplier Using Weakly Dual Basis Over $GF(2^{m})$

In this paper, we present a new method to compute the Mastrovito matrix for
GF
(2
^m
) generated by an arbitrary irreducible polynomial using weakly dual basis of shifted polynomial basis. In particular, we derive the explicit formulas of the proposed multiplier for special type of irreducible pentanomial
x
^m
+
x
^k3
+
x
^k2
+
x
^k1
+1 with
k
₁
<;
k
₂
≤ (
k
₁
+
k
₃
)/2 <;
k
₃
<; min(2
k
₁
,
m
/2). As a result, the time complexity of the proposed multiplier matches or outperforms the previously known results. On the other hand, the number of XOR gates of the proposed multiplier is slightly greater than the best known results.