Simple Encrypted Arithmetic Library - SEAL v2.1

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), so that one can perform certain 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 a one particular type of operation is very strong, however, and instead a much more powerful fully homomorphic encryption scheme, that respects two algebraic operations between the plaintext and ciphertext spaces, would be needed for many interesting applications. The first such encryption scheme was presented by Craig Gentry in his famous work [16], and since then researchers have introduced a number of new and more efficient fully homomorphic encryption schemes. Despite the promising theoretical power of homomorphic encryption, the practical side still remains somewhat underdeveloped. Recently new implementations, new data encoding techniques, and new applications have started to improve the situation, but much remains to be done. In 2015 we released the Simple Encrypted Arithmetic Library SEAL with the 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 library is available at http://sealcrypto.codeplex.com, and is licensed under the MSR License Agreement. Recently a large number of major changes were implemented in SEAL, and the new version was released as SEAL v2.0. This involved major changes in the public API, and a change of the underlying encryption scheme. Since the release of SEAL v2.0 several improvements have been made. Most of these are very important performance-related improvements, but there are also a few changes and additions to the public API. These improvements have now been released as SEAL v2.1. In this document we describe in detail this new release, and hope to provide a practical guide to using homomorphic encryption for a wide audience. The reader is also advised to go over the code examples that come with the library, and to read through the detailed comments. For users of previous versions of SEAL (both v2.0 and earlier) we hope to provide clear instructions for how to port old code to use SEAL v2.1. An introductory paper to an older version of SEAL was given in [12], which the user new to SEAL v2.1 may also find helpful as large parts of the API have remained unchanged. This document is an extension of a similar document that accompanied the release of SEAL v2.0 [19].