LWE-Based FHE with Better Parameters

Fully homomorphic encryption allows a remote server to perform computable functions over the encrypted data without decrypting them first. We propose a public-key fully homomorphic encryption with better parameters from the learning with errors problem. It is a public key variant of Alperin-Sheriff and Peikert's symmetric-key fully homomorphic encryption (CRYPTO 2014), a simplified symmetric version of Gentry, Sahai and Waters' (CRYPTO 2013), and is based on a minor variant of Regev's public-key encryption scheme (STOC 2005) which may be of independent interest. Meanwhile, it can not only homomorphically handle "NAND" circuits, but also conform to the traditional wisdom that circuit evaluation procedure should be a naive combination of homomorphic additions and multiplications.