Fast Private Set Intersection from Homomorphic Encryption

Question

I encountered a question while reading an article. My understanding is that fully homomorphic encryption supports ciphertext addition and multiplication. Why does the basic protocol given in this article include ciphertext subtracted by plaintext?

Answer 1

In FHE schemes, an operation between a plaintext and a ciphertext can be performed by first encrypting the plaintext using the scheme's public key and then evaluating the corresponding operations (e.g., ADD or MULT) over ciphertexts.

However, because the plaintext is "known" (in this case it is known to the sender), in many cases it is not necessary to compute a random ciphertext, which can be more efficient in practice.