Small plaintext modulus

Library Questions
1

Disclaimer: I’m fairly new to FHE and OpenFHE.

I am building an application that works on categorical data with relatively few categories that fit in 8 bits. I want to use Fermat’s little theorem to generate encrypted 1’s for elements that are equal and encrypted 0’s otherwise. To that end, I attempted to change the plaintext modulus to 257, a small prime that fits my data, but I get the error below. I’m not sure what m refers to. I looked in the CCParams but didn’t see anything with the value of 16384.

Please provide a primeModulus(q) and a cyclotomic number(m) satisfying the condition: (q-1)/m is an integer. The values of primeModulus = 257 and m = 16384 do not satisfy this condition

2

OpenFHE uses CRT packing based on linear terms decomposition. In other words, we use moduli that give the maximum number of slots (= ring dimension). So the minimum plaintext modulus has to be a prime that is congruent to 1 mod m (in other words it is at least m + 1 or larger).

3

Thanks for the explanation. The plaintext modulus 65537 is working fine for my purposes. If I understand you correctly, decreasing the plaintext modulus requires decreasing the number of slots and ultimately the security level as well.

4

Is there a way to bypass this constraint? Perhaps we can set the parameters manually?

I’m not interested in optimizing for slots for my use case, and would much rather work with tight parameters.