Comment by 3s

SHE vs FHE has nothing to do with security. Instead, it’s about how many operations (eg homomorphic multiplications and additions) can be performed before the correctness of the scheme fails due to too much noise accumulating in the ciphertext. Indeed all FHE schemes are also SHE schemes.

What typically makes FHE expensive computationally is a “bootstrapping” step for removing the noise that accumulated after X operations and threatening correctness. After bootstrapping you can do another X operations. Rinse and repeat until you finish the computation to you want to perform.