Large Plaintext moduli

[rw0x0]

Hi guys, what does it take to modify the library to allow large plaintext primes of up to 256 bit? Thank you!

[Pro7ech]

Before I consider providing an answer, I have the following question: do you actually need the plaintext modulus to be a prime, or can it be a composite?

I guess you do (I suspect you are trying to do ECC), but just making sure

[rw0x0]

Thanks for the answer! If I would write a custom encode/encrypt and decode/decrypt with a larger plaintext modulus, the ciphertext domain should mostly be the same (at least for textbook BGV) or am I missing something? In the first step I would just need additions and ciphertext-plaintext multiplications in the encrypted domain, so all the complicated ciphertext-ciphertext multiplication stuff can be ignored in the beginning

[Pro7ech]

Encrypt decrypt doesn't need to be modified. You'll need to adapt the encoder, and all ops in the evaluator that use the plaintext modulus at some point. The hardest one will be the basis extender. And you'll also need to implement a ring that accepts u256. Probably it's best to already factorize p-1 to speed up the generation of the ring

[Pro7ech]

You will also need to update the scale in rlwe, as it is only u128

[Pro7ech]

Do you need batching? I.e. packing multiple plaintext values. If you don't then you could hack something without having to modify too much the encoder and implement a basis reduction with big.int

[rw0x0]

thanks for the detailed answer, will definitely look at it. Regarding batching, I intend to have it at some point, but I did not even check yet, whether my prime allows for it. But you might be right, a first version without batching might be easier to implement... Thanks again!