# Polynomial Multiplication and Modulo Operation complexity [duplicate]

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 $\Bbb F_q[x]$.

• What did you try? Where did you get stuck? We're happy to help you understand the concepts but just solving exercises for you is unlikely to achieve that. What have you tried? What prevents you from answering this? Do you already know how many bit operations does it take to do a ring addition? a ring multiplication? If not, what research have you done, and what effort have you made to attempt to understand? Also, please ask only one question per post. If you can address this feedback, please edit the question accordingly. – D.W. Oct 26 '16 at 7:35
• – D.W. Oct 26 '16 at 7:38
• @D.W. I am sorry but you really are getting on my nerves. None of your suggestions is useful please step down as moderator if you prefer to be hasty. – T.... Oct 27 '16 at 22:45