# For the LTV-FHE scheme, after how many additions should modulus switching be used?

From the LTV-FHE paper I find out that after every multiplication there must be a modulus switch to mitigate the noise in the resulting ciphertext, besides relinearization.

But, assuming the ciphertexts to be summed are the result of many operations and we have consumed many levels of the moduli ladder, that means that the room for noise is smaller. ( The assumption that the room for noise is getting smaller may be wrong, I haven't found any proof yet, is my personal observation.)

So, if we evaluate homomorphically many additions of ciphertexts like those aforementioned, should we use modulus switching to cut the noise before wrap around ?

• Concretely: Set up ciphertexts so that addition increases magnitude of noise by (fixed) $poly(\lambda)$ (additively). Set noise threshold to $2^\lambda.$ Aug 19 '16 at 12:06