I'm using Pailier Cryptosystem as an additive homomorphic system in my scenario. I have two parties: Alice and Bob. Alice has one pair of (SK, Pk) keys. She encryptes one value using her public key and sends it to Bob. In Bob's side, we need to define whether this value is negative or positive. How can I achieve that?
Assume that there is a such function $f$, that can determine the sign of the number within the ciphertext .
Let the message space $P$ Using the binary technique, then an adversary can actually find the message as; where $c$ is the ciphertext
if $f( c - E_p( |P|/2 ))$ > 0 if $f( c - E_p( |P| ))$ > 0 else if $f( c - E_p( 0 ))$ > 0...
As usual binary search.