I am currently reading Homomorphic Encryption Standard.
May I ask that for table 1 in the link, why increasing the security level will yield a smaller ciphertext size (log q)?
I attach a screenshot below enter image description here Thanks a lot!


1 Answer 1


In simple terms, since smaller q (i.e. bit size) gives higher security level, and ciphertext is presented in modolus q form, therefore when keeping other parameters the same, smaller q gives smaller ciphertext and higher security level at the same time.

  • $\begingroup$ Thanks for the reply! So by increasing the log q to tolerate more homomorphic operations, does it means that this indeed decrease the security level? $\endgroup$
    – js wang
    Oct 26, 2023 at 21:01
  • $\begingroup$ @jswang to some extent yes $\endgroup$
    – 9f241e21
    Oct 28, 2023 at 2:28

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