Given two polynomials of degree $n$ and $m$ over $\Bbb F_q[x]$ it takes about $O((n+m)\log ((n+m)))$ operations ring operations over $\Bbb F_q[x]$ to multiply them.
What is the corresponding bit operations?
What is the corresponding ring and bit operation count for remainder operations in $\Bbb F_q[x]$.
