I am currently playing around with some of the Python FHE libraries and found out that, e.g. TenSeal (SEAL) is able to perform "only" 8 ciphertext-ciphertext multiplications on the same ciphertext (8x1 Vector) (c1 = c1*c2 in a loop) before the noise threshold is surpassed and decryption fails.
The parameters I set for this are:
plain_modulus=536903681 using the BFV Scheme.
Is it even possible to perform arbitrary amounts of operations on the same ciphertext, assuming runtime is irrelevant? I understand, that multiplication operations increase noise significantly, but methods like bootstrapping and relinearization do not seem to decrease the noise in a way, that would allow an unlimited amount of computations, right?