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I want to find out how many bit operations are performed for encryption in AES-128 with messages size $128$ bits.

For public key encryptions such as RSA and ElGamal, I know that number of bit operations required are $O(n^3)$ if the key considered has $n$ bits.

Are these equal to $O(1)$?

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    $\begingroup$ This question has been asked before. No, we don't use Big-Oh for symmetric ciphers, And that really depends on the implementation, use of a pre-computed table or not, etc. The only article that really counted is TOA et. al They went on this to show that their attack better than the brute-force. $\endgroup$
    – kelalaka
    Mar 4, 2021 at 17:14
  • $\begingroup$ And, for the RSA, Why it is $O(n^3)$? $\endgroup$
    – kelalaka
    Mar 4, 2021 at 17:17
  • $\begingroup$ RSA involves modular exponentiation. So, if we use square and multiply algorithm, then it is so. It can further be optimized. $\endgroup$
    – PAMG
    Mar 4, 2021 at 17:20
  • $\begingroup$ It is $\mathcal{O}(3\cdot n^2)$ at most whem $e=3$ $\endgroup$
    – kelalaka
    Mar 4, 2021 at 17:23
  • $\begingroup$ But e is not 3, in general. What if I want to send a same messages to more than 3 entities? $\endgroup$
    – PAMG
    Mar 5, 2021 at 16:39

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