Other meanings of Homomorphic Encryption
Cryptography
Homomorphic encryption is a cryptographic technique that enables computations to be performed on encrypted data without first decrypting it. The result of the computation remains encrypted and, when decrypted, matches the result of the same operations performed on the plaintext. This property allows sensitive data to be processed in untrusted environments, such as cloud servers, while preserving privacy. The concept was first proposed by Rivest, Adleman, and Dertouzos in 1978, shortly after the invention of RSA, but practical implementations remained elusive for decades. Modern schemes are categorized into partially, somewhat, leveled, and fully homomorphic encryption, with fully homomorphic encryption (FHE) supporting arbitrary computations. The field has advanced significantly since Craig Gentry's breakthrough in 2009, leading to real-world applications in healthcare, finance, and machine learning.
The idea of computing on encrypted data dates to 1978, when Ronald Rivest, Leonard Adleman, and Michael Dertouzos proposed a 'privacy homomorphism' in a memo that explored the possibility of processing encrypted information without exposing it. Early attempts, such as the RSA scheme, were partially homomorphic, supporting only multiplication of ciphertexts. Paillier's scheme (1999) added additive homomorphism, and the Boneh-Goh-Nissim scheme (2005) supported both addition and one multiplication. These schemes were limited in the types of functions they could evaluate, and none could handle arbitrary computations. The field remained largely theoretical until Craig Gentry's 2009 dissertation introduced the first fully homomorphic encryption scheme, using ideal lattices and a technique called bootstrapping to reduce the noise that accumulates during operations. Gentry's work was a landmark, proving that FHE was possible and sparking a decade of intense research into practical implementations.
Modern homomorphic encryption schemes are built on the learning with errors (LWE) problem and its ring variant (RLWE), which provide strong security guarantees and enable efficient operations. The BGV scheme (Brakerski, Gentry, Vaikuntanathan, 2011) and the BFV scheme (Brakerski/Fan-Vercauteren) are among the most widely used, supporting leveled homomorphic encryption where the depth of the circuit is known in advance. The CKKS scheme (Cheon, Kim, Kim, Song, 2017) is designed for approximate arithmetic on real numbers, making it popular for machine learning applications. Bootstrapping, the process of refreshing ciphertexts to reduce noise, remains computationally expensive but has been optimized significantly; the FHEW and TFHE schemes (2014–2016) introduced fast bootstrapping for Boolean circuits, enabling practical applications like private database queries. Libraries such as Microsoft SEAL, HElib, and PALISADE provide open-source implementations, and standardization efforts by the HomomorphicEncryption.org consortium have produced security guidelines.
Homomorphic encryption is used in scenarios where data privacy is paramount, such as healthcare analytics, financial fraud detection, and secure voting. In healthcare, it allows researchers to compute statistics on encrypted patient records without accessing raw data, as demonstrated in genome-wide association studies. In finance, it enables banks to perform risk assessments on encrypted customer data without exposing individual transactions. Machine learning models can be trained and evaluated on encrypted data, with recent work showing that neural networks can operate on encrypted images with reasonable accuracy. However, the overhead is substantial: ciphertexts are typically hundreds of times larger than plaintexts, and computations can be orders of magnitude slower. Noise management, parameter selection, and the need for specialized hardware are ongoing challenges. Researchers are exploring hardware accelerators, such as FPGAs and GPUs, to mitigate performance issues, and hybrid approaches combine homomorphic encryption with secure multiparty computation to improve efficiency.
Beyond the mainstream narrative, several niche aspects of homomorphic encryption are notable. The concept of 'somewhat homomorphic encryption' (SHE) allows a limited number of operations, and the distinction between leveled and fully homomorphic is often blurred in practice. The first FHE scheme was based on ideal lattices, but later schemes like GSW (Gentry, Sahai, Waters, 2013) simplified the construction using matrix operations. Bootstrapping, while theoretically elegant, is so costly that many applications avoid it entirely, using leveled schemes instead. The CKKS scheme, despite its approximate nature, has been used in privacy-preserving neural network inference, and its security analysis is still an active area of research. There is also a lesser-known variant called 'functional encryption' that allows specific functions to be computed on encrypted data, but it is distinct from homomorphic encryption. The history includes early patents by IBM and NTT, and the first practical demonstration of FHE on a real-world problem was a 2012 paper on encrypted search. The field has also seen contributions from cryptographers like Vinod Vaikuntanathan, who co-authored several foundational schemes, and the annual Workshop on Encrypted Computing and Homomorphic Cryptography (ECH) is a dedicated venue for the community.
Homomorphic encryption is a cornerstone of privacy-enhancing technologies, with ongoing research aimed at making it practical for widespread use.
Help improve the encyclopedia. Reports go straight to the site manager.