I want to implement the multiplication using normal basis in the binary field $GF(2^n)$ (where n=163, 233 for example). The multiplication with normal basis is performed by $c_0=A*M*B^T$, where $M$ is an $n\times n$ matrix, and $c_0$ is one bit of $C=A*B$.
Is there any software or program that can support such multiplication with normal basis (especially the Gaussian normal basis (GNB))? Or can produce the matrix $M$?