I'm trying to sample HE ciphertexts which serve as ciphertexts encrypting some random values. I have realized a example program using Microsoft SEAL, which implements a variant of BFV scheme. Unfortunately, the ''noise budget'' of these uniformly-distributed ciphertexts is zero and thus they cannot support any further homomorphic evaluation. However, when I draw these ciphertexts from discrete Guassian distribution (with mean = 0), they have non-zero ''noise budget'' and work fine.
I'm quite confused about this result. Since BFV scheme is IND-CPA secure, its valid fresh ciphertexts should be indistinguishable from malformed ones (i.e., drawn from uniform distribution). However, the experiment result shows that a uniformly-distributed ciphertext does not form a valid ciphertext of BFV scheme with overwhelming probability.
Is there something wrong? Many thanks.