Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption

We present several new and fairly practical public-key encryption schemes and prove them secure against adaptive chosen ciphertext attack. One scheme is based on Paillier’s Decision Composite Residuosity assumption, while another is based in the classical Quadratic Residuosity assumption. The analysis is in the standard cryptographic model, i.e., the security of our schemes does not rely on the Random Oracle model. Moreover, we introduce a general framework that allows one to construct secure encryption schemes in a generic fashion from language membership problems that satisfy certain technical requirements. Our new schemes fit into this framework, as does the Cramer-Shoup scheme based on the Decision Diffie-Hellman assumption.