Hi
In my case, I would need to do a lot of multiplications, therefore leading to the need of larger logN like 16,17 or maybe even 18. Hence, I would like to know what’s the range of logPQ for certain security level (128,196 etc.). I cant find a guide for selecting such large N.
Thanks for your time!
What scheme are you using?
If you are using CKKS, it might be more efficient to bootstrap after consuming the multiplicative depth.
This paper has some parameters for up to N = 2^{17}.
For N > 2^{16}, you can use the table 4.2 from https://eprint.iacr.org/2024/463.pdf (it includes the threshold for N=2^{17}). Although this document is still work in progress (after review by the community, it will eventually replace https://homomorphicencryption.org/wp-content/uploads/2018/11/HomomorphicEncryptionStandardv1.1.pdf), the table can be used for practical applications. As @Caesar pointed out, CKKS bootstrapping could also be used to keep N \leq 2^{17}