Simple Encrypted Arithmetic Library - SEAL v2.2

Traditional encryption schemes, both symmetric and asymmetric, were not designed to respect the algebraic structure of the plaintext and ciphertext spaces. Many schemes, such as ElGamal (resp. e.g. Paillier), are multiplicatively homomorphic (resp. additively homomorphic), and can be used to perform limited types of computations directly on the encrypted data and have them pass through the encryption to the underlying plaintext data, without requiring access to any secret key(s). The restriction to one single operation is very strong, however, and instead a much more powerful fully homomorphic encryption scheme that respects both additions and multiplications would be needed for many interesting applications. The first such encryption scheme was invented by Craig Gentry in 2009 [21], and since then researchers have introduced a number of new and more efficient fully homomorphic encryption schemes [11, 10, 7, 9, 20, 30, 5, 23]. Despite the promising theoretical power of homomorphic encryption, the practical side remained underdeveloped for a long time. Recently new implementations, new data encoding techniques, and new applications have started to improve the situation, but much remains to be done. In 2015 the first version of the Simple Encrypted Arithmetic Library SEAL was released, with the specific goal of providing a well-engineered and documented homomorphic encryption library, with no external dependencies, that would be easy to use both by experts and by non-experts with little or no cryptographic background. The underlying encryption scheme, and some of the public API, were changed in 2016, and the new version was released as SEAL v2.0. Soon after the release of SEAL v2.0 significant performance updates and bug fixes were implemented, and released as SEAL v2.1. Along with SEAL v2.1, an experimental branch of the library was released. This experimental branch, along with several further updates, has now been released as SEAL v2.2. This documents describes the core features of SEAL v2.2, and attempts to provide a practical guide to using homomorphic encryption for a wide audience. We strongly advise the reader to go over the code examples that come with the library, and to read through the detailed comments accompanying the examples. For users of previous versions of SEAL (both v2.1 and earlier) we hope to provide clear instructions for how to port old code to use SEAL v2.2. The library is available at http://sealcrypto.codeplex.com, and is licensed under the MSR License Agreement.