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Symmetric Somewhat Homomorphic Encryption over the Integers

We describe a symmetric variant of homomomorphic encryption scheme by van Dijk et al. [DGHV10], semantically secure under the error-free approximate-GCD problem. We also provide the implementation of the scheme as a C/C++ library. The scheme allows to perform “mixed” homomorphic operations on ciphertexts and plaintexts, eliminating the need to encrypt new ciphertexts using the public key for some applications, specifically, in secure function evaluation setting. Compared to the original scheme and other homomorphic encryption schemes, the properties of the symmetric variant enable for smaller communication cost for applications like privacy-preserving cloud computing, and private information retrieval.