Quiz Entry - updated: 2026.07.14
What are the three levels of the homomorphic encryption spectrum?
Partially (PHE), Somewhat (SWHE), and Fully Homomorphic Encryption (FHE) — increasing in capability and cost.
* The HE spectrum: capability and cost both rise from PHE to SWHE to FHE. *
| Level | What it supports | Trade-off |
|---|---|---|
| Partially (PHE) | One operation type, unlimited times (e.g. only multiplications, or only additions) | Fast, practical, limited use cases. RSA and Paillier are classic examples. |
| Somewhat (SWHE) | Both add and multiply, but only a limited number of operations | "Noise" builds up and eventually corrupts the result. |
| Fully (FHE) | Arbitrary computations, unlimited depth | The holy grail — but very slow. Enabled by Gentry's 2009 "bootstrapping" breakthrough. |
Why the limits exist: HE ciphertexts accumulate noise with each operation. FHE's bootstrapping "refreshes" the ciphertext to remove noise, allowing unlimited computation — at a heavy performance price.