I am aware of this attack that applies to PHE (partially homomorphic encryption) given the attacker has access to a trusted oracle that can
Convert (i.e decrypt and re-encrypt) between
AHE (additive, e.g. Paillier) and
DET (deterministic) schemes.
1. Get ciphertexts E(0) in DET and E(1) in AHE 2. i = 0 3. Convert E(x) to DET encryption 4. Compare E(x) to E(0) 5. If equal, print i and exit 6. Convert E(x) to AHE encryption 7. Add E(x) and E(1) using homomorphic property 8. i = i + 1 9. Goto 3
My question is how is this attack avoided in FHE (fully homomorphic encryption) which allows arbitrary computations (e.g adding and comparing) on ciphertexts.