What is Homomorphic Encryption (HE)?

Encryption that lets you perform computations directly on ciphertext, producing an encrypted result that — once decrypted — matches the result of doing the same operations on the plaintext.

* HE message flow: the server computes on ciphertext and never decrypts. *

* Computing on encrypted data without decrypting it. — Aaadir, CC0, via Wikimedia Commons. *

It's the most radical answer to the data-in-use problem: the data is never decrypted during processing. A cloud server can run analytics on your encrypted data and hand back an encrypted answer it could never actually read.

The core property (illustrative):

$$\text{Dec}(\,\text{Enc}(a) \oplus \text{Enc}(b)\,) = a + b$$

You sent only ciphertext, the server computed on ciphertext, and you decrypt to get the true sum — the server learned nothing.

Tip: Think "computing inside a locked glovebox" — the worker manipulates the contents through gloves without ever opening the box.

Go deeper:

• Homomorphic encryption (Wikipedia) — the partial/somewhat/fully spectrum and Gentry's bootstrapping.