Galois Keys for N=1024,2048

[RasoulAM]

Why is it not possible to generate Galois keys for N=1024 and N=2048? Is there a theoretical limitation or is it not implemented in the library? If it's a theoretical limitation, can you point me to a paper which explains the limitation?

Thanks

[fionser]

Current SEAL implementation uses one prime for the noise control (ie., the so call special prime). On the other hand, for small Ns (eg. 1024, 2048), we can not have many bits for the modulus already to make sure the scheme is secure. As a result, SEAL do not generate Galois keys for such small Ns.

However, if you need Galois for such smaller parameter, you might need to implement the digit-decomposition version of Galois key which does not need the extra special prime. Check out the ancient SEAL