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

• We construct a homomorphic encryption scheme with CCA2 security but without random oracle.
• We present a novel concept of preventing or blocking adaptive chosen ciphertext attacks.
• We examine how to deal with CCA2 over homomorphic encryption scheme, while keeping homomorphism.

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).