Homomorphic authenticated encryption secure against chosen-ciphertext attack

We study homomorphic authenticated encryption, where privacy and authenticity of data are protected simultaneously. We define homomorphic versions of various security notions for privacy and authenticity, and investigate relations between them. In particular, we show that it is possible to give a natural definition of IND-CCA for homomorphic authenticated encryption, unlike the case of homomorphic encryption. Also, we construct a simple homomorphic authenticated encryption scheme supporting arithmetic circuits, which is chosen-ciphertext secure both for privacy and authenticity. Our scheme is based on the error-free approximate GCD assumption