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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. eg 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 most applications. The first such encryption scheme was presented by Craig Gentry in his famous work [14], 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 …