basics of homomorphic encryption

Fully homomorphic encryption, or simply homomorphic encryption, refers to a class of encryption methods envisioned by Rivest, Adleman, and Dertouzos already in 1978, and first constructed by Craig Gentry in 2009. Homomorphic encryption differs from typical encryption methods in that it allows computation to be performed directly on encrypted data without requiring access to a secret key. The result of such a computation remains in encrypted form, and can at a later point be revealed by the owner of the secret key.


Cheap cloud computing and cloud storage have fundamentally changed how businesses and individuals use and manage their data. Traditional encryption methods, such as AES, are extremely fast, and allow data to be stored conveniently in encrypted form. However, to perform even simple analytics on the encrypted data, either the cloud server needs access to the secret key, which leads to security concerns, or the owner of the data needs to download, decrypt, and operate on the data locally, which can be costly and create a logistic challenge. Homomorphic encryption can be used to simplify this scenario considerably, as the cloud can directly operate on the encrypted data, and return only the encrypted result to the owner of the data. More complex application scenarios can involve multiple parties with private data that a third party can operate on, and return the result to one or more of the participants to be decrypted.

The yearly iDASH competition challenges the research community to push the limits and extend homomorphic encryption to new use-cases in the field of genome privacy. Several concrete application scenarios will be presented in the upcoming white papers.


The security of the most practical homomorphic encryption schemes is based on the Ring-Learning With Errors (RLWE) problem, which is a hard mathematical problem related to high-dimensional lattices. Namely, the security assumption of these encryption schemes states that if the scheme can be broken efficiently, then the RLWE problem can be solved efficiently. A long line of peer-reviewed research confirming the hardness of the RLWE problem gives us confidence that these schemes are indeed as secure as any standardized encryption scheme.


There are several reasons why we think this is the right time to standardize homomorphic encryption.

  • There is already dire need for easily available secure computation technology, and this need will be getting stronger as more companies and individuals switch to cloud storage and computing. Homomorphic encryption is already ripe for mainstream use, but the current lack of standardization is making it difficult to start using it.
  • Specifically, the current implementations are not easy enough to use by non-experts. The standard will push to uniformize and simplify their API, and educate the application developers about to use them.
  • The security properties of RLWE-based homomorphic encryption schemes can be hard to understand. The standard will present the security properties of the standardized scheme(s) in a clear and understandable form.


Several open-source implementations of homomorphic encryption schemes exist today. Below is an incomplete list. If you would want to see your implementation being added, please contact us at

  • cuHE: This library explores the use of GPGPUs to accelerate homomorphic encryption.
  • HeaAn: This library implements a scheme with native support for fixed point approximate arithmetic.
  • HELib: This is an early and widely used library from IBM that supports the BGV scheme and bootstrapping.
  • Λ ○ λ (pronounced “L O L”): This is a Haskell library for ring-based lattice cryptography that supports FHE.
  • NFLlib: This library is an outgrowth of the European HEAT project to explore high-performance homomorphic encryption using low-level processor primitives.
  • PALISADE: This is a general lattice encryption library that supports several lattice encryption schemes, including multiple homomorphic encryption schemes.
  • SEAL: This is a widely used library from Microsoft that supports the FV scheme.