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 $\Bbb F_q[x]$.

  • $\begingroup$ 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. $\endgroup$
    – D.W.
    Oct 26 '16 at 7:35
  • $\begingroup$ @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. $\endgroup$
    – Mr.
    Oct 27 '16 at 22:45
  • $\begingroup$ My goal is to explain our community norms and expectations, and to help you improve your question so it can be suitable here; if you have not found that helpful, I'm sorry to hear that. I don't think I'm being hasty -- I'm taking time to help you understand how you can adjust your question to be suitable here. If you have concerns about my actions as moderator, feel free to flag my comment with a custom comment explaining your specific concerns so other moderators can review them; post on meta; or use the "contact us" form below if you'd like to ask Stack Exchange to review my actions. $\endgroup$
    – D.W.
    Oct 27 '16 at 23:32
  • $\begingroup$ @D.W. sorry your wall of text made me think that way. I will try to improve. $\endgroup$
    – Mr.
    Oct 27 '16 at 23:33