Moni Naor and Moti Yung present a public-key cryptosystem that is provably secure against chosen ciphertext attacks (CCAs). The system relies on a public-key cryptosystem secure against passive eavesdropping and a non-interactive zero-knowledge proof system in the shared string model. The scheme uses probabilistic encryption and non-interactive zero-knowledge proofs to ensure consistency of ciphertexts and prevent decryption attacks. The public key consists of two encryption keys and a shared random string. To encrypt a message, it is encrypted using both keys, and a proof is appended to ensure consistency. Decryption involves verifying the proof before decrypting the message. The system is proven secure against CCAs by showing that breaking it would imply either the probabilistic encryption scheme is distinguishable or the non-interactive zero-knowledge proof system is not zero-knowledge. The scheme is based on quadratic residuosity intractability and is constructed using a combination of probabilistic encryption and non-interactive zero-knowledge proofs. The security is proven by reducing the problem to known hardness assumptions and showing that any successful attack would violate these assumptions.Moni Naor and Moti Yung present a public-key cryptosystem that is provably secure against chosen ciphertext attacks (CCAs). The system relies on a public-key cryptosystem secure against passive eavesdropping and a non-interactive zero-knowledge proof system in the shared string model. The scheme uses probabilistic encryption and non-interactive zero-knowledge proofs to ensure consistency of ciphertexts and prevent decryption attacks. The public key consists of two encryption keys and a shared random string. To encrypt a message, it is encrypted using both keys, and a proof is appended to ensure consistency. Decryption involves verifying the proof before decrypting the message. The system is proven secure against CCAs by showing that breaking it would imply either the probabilistic encryption scheme is distinguishable or the non-interactive zero-knowledge proof system is not zero-knowledge. The scheme is based on quadratic residuosity intractability and is constructed using a combination of probabilistic encryption and non-interactive zero-knowledge proofs. The security is proven by reducing the problem to known hardness assumptions and showing that any successful attack would violate these assumptions.