On CCA-Secure Fully Homomorphic Encryption

It is well known that any encryption scheme which supports any form of homomorphic operation cannot be secure against adaptive chosen ciphertext attacks. The question then arises as to what is the most stringent security definition which is achievable by homomorphic encryption schemes. Prior work has shown that various schemes which support a single homomorphic encryption scheme can be shown to be IND-CCA1, i.e. secure against lunchtime attacks. In this paper the authors extend this analysis to the recent fully homomorphic encryption scheme proposed by Gentry, as refined by Gentry, Halevi, Smart and Vercauteren.