Homomorphic encryption

In short: With homomorphic encryption you can compute on encrypted data without decrypting it first. Only the result is decrypted.

In more detail: A cloud service could thus calculate sums or models on data it never sees in plaintext.

In Depth

• Idea: Dec(Enc(a) ⊕ Enc(b)) = a + b. Computing on the ciphertexts corresponds to computing on the plaintexts.
• Levels: Partially homomorphic (only addition or only multiplication, for example RSA and Paillier), fully homomorphic (FHE, arbitrary computations, since Gentry’s scheme in 2009).
• Cost: FHE is still orders of magnitude slower than plaintext computation and needs much memory. It suits selected tasks.
• Applications: Privacy for medical data, voting, evaluations across several parties, search in encrypted databases.
• Related: Secure multi-party computation (MPC), zero-knowledge proofs and confidential computing pursue similar goals by other means.
• Libraries: Microsoft SEAL, OpenFHE, TFHE.

See also: Asymmetric encryption