A homomorphic encryption scheme with adaptive chosen ciphertext security but without random oracle ☆

In this study, we consider the problem of constructing a homomorphic encryption scheme that is secure against adaptive chosen ciphertext attack (CCA2). This type of scheme has many applications in secure multi-party computation, electronic voting, and cloud storage and computation. We present an encryption scheme, based on the composite degree residuosity classes, which can block CCA2 while maintaining homomorphism. Our cryptosystem, which is based on standard modular arithmetic, is provable with indistinguishable security under CCA2. An additional contribution of this study is a new definition of preventing CCA2 (or blocking CCA2).