International Association
for Cryptologic Research

We extend the fully homomorphic encryption scheme over the integers of van Dijk et al. (DGHV) to batch fully homomorphic encryption, i.e. to a scheme that supports encrypting and homomorphically processing a vector of plaintext bits as a single ciphertext. Our variant remains semantically secure under the (error-free) approximate GCD problem. We also show how to perform arbitrary permutations on the underlying plaintext vector given the ciphertext and the public key. Our scheme offers competitive performance: we describe an implementation of the fully homomorphic evaluation of AES encryption, with an amortized cost of about 12 minutes per AES ciphertext on a standard desktop computer; this is comparable to the timings presented by Gentry et al. at Crypto 2012 for their implementation of a Ring-LWE based fully homomorphic encryption scheme.