CyberGlossary

Cryptography

Homomorphic Encryption

Also known as: FHE, Fully Homomorphic Encryption

Definition

An encryption scheme that allows computations to be performed directly on ciphertexts, producing encrypted results that match the operations on the underlying plaintexts.

Homomorphic Encryption (HE) is a form of public-key cryptography that supports arithmetic operations on ciphertexts without decryption: decrypting the result yields the same answer as performing the operation on the plaintext. Partially Homomorphic schemes (RSA, ElGamal, Paillier) support a single operation, Somewhat Homomorphic schemes a bounded depth of operations, and Fully Homomorphic Encryption (FHE) — pioneered by Gentry in 2009 and now implemented in BFV, BGV, CKKS and TFHE on top of the Ring-LWE problem — supports arbitrary depth via bootstrapping. HE enables privacy-preserving cloud computation, private machine-learning inference, encrypted database queries and secure multiparty computation, but is several orders of magnitude slower and more memory-intensive than plaintext computation, with ongoing research and standardization (HomomorphicEncryption.org, ISO/IEC) reducing the cost.

Examples

  • Microsoft SEAL implements BFV and CKKS for encrypted analytics on cloud data.
  • Zama's TFHE-rs is used to evaluate machine-learning models directly on encrypted inputs.

Related terms