Overview
ISO/IEC 18033-6:2019 - "IT Security techniques - Encryption algorithms - Part 6: Homomorphic encryption" - defines standardized mechanisms for homomorphic encryption. The standard specifies two mechanisms (Exponential ElGamal and Paillier) and, for each, details the processes for parameter and key generation, encryption, decryption, and homomorphic operations on ciphertexts. Annex A assigns object identifiers for the mechanisms and Annex B contains numerical examples.
Key topics and technical requirements
- General model
- Three roles: encryptor, decryptor, and operator (third party performing computation on ciphertext).
- Public parameters and public key are available to encryptor/operator; private key is held by decryptor.
- Algorithms defined
- KeyGen(k) - produce (pub.key, sec.key, parameters) given a security parameter k.
- Encrypt(m, pub.key, parameters) - probabilistic encryption that maps plaintext group elements to ciphertexts.
- Decrypt(c, sec.key, parameters) - deterministic decryption recovering plaintext group elements.
- Functional requirements
- Correctness: Decrypt(Encrypt(m)) = m.
- Homomorphic property: There exists a group operation on plaintexts and a corresponding operation on ciphertexts such that Decrypt(c1 ⨀ c2) = m1 • m2.
- Mechanism specifics (as specified by the standard)
- Exponential ElGamal: parameters (p, q, g), key generation, encryption and decryption algorithms are specified; ciphertexts support coordinate-wise multiplication modulo p and plaintexts are group elements. The document discusses practical uses (e.g., small-message scenarios such as electronic elections) and notes parameter sizes are driven by the security parameter k.
- Paillier: the standard likewise specifies parameter/key generation, encryption, decryption and homomorphic operations (object identifier and numerical examples provided).
Practical applications and who uses this standard
- Applications
- Privacy-preserving computation and analytics on encrypted data (cloud computation, secure aggregation, private voting).
- Use cases where operators should compute on ciphertexts without accessing plaintexts (outsourced computation, secure multi-party workflows).
- Who should use ISO/IEC 18033-6
- Cryptographic library developers and implementers.
- Security architects designing systems that require homomorphic operations.
- Regulators, standards bodies and auditors evaluating compliant cryptographic implementations.
- Researchers and engineers implementing Exponential ElGamal or Paillier according to standardized procedures.
Related standards
- Other parts of the ISO/IEC 18033 series and ISO/IEC JTC 1/SC 27 documents (references used for terminology, parameter generation and related encryption algorithm standards).
Keywords: ISO/IEC 18033-6, homomorphic encryption, Exponential ElGamal, Paillier, encryption algorithms, IT security techniques, key generation, homomorphic property.
