Hello,
In the encoding procedure of CKKS, the input vector is first scaled up by a large number (which is commonly called scale and determines the precision) and then encoded into a polynomial. I would like to set different scales for each input ciphertext and constants in the same program, and I am wondering if that’s possible in OpenFHE.
SEAL implements this feature: their CKKS encoding operation is encode(values, scale, destination) where scale is used to scale up the input. As an illustration, figure 1 in the EVA paper shows that scales are different for each input, ranging from 2^{30} to 2^{60}.
In my understanding, the equivalent for scale in the CKKS encoding implementation of OpenFHE is
scFact = cryptoParams->GetScalingFactorReal(level)
which is assigned to powP in the Plaintext::Encode function. However, this number seems to be fixed for each level. From a theory perspective, according to [KPP21], the Encode function scales up the input by \Delta which is also a constant. So if I am not mistaken, this means that it is impossible to set different scales for each input in OpenFHE. I would like to ask for a kind confirmation or clarification on this.
As a side note, I would like this feature because I am working with FHE compilers with scale management. Smaller scaling factors mean more multiplication depth and sparser Rescaling/Bootstrapping (and thus better runtime performance) with the same set of modulus, so one can fine-tune the scaling factors to balance performance and precision.
Thank you,
Zhengyuan Su