Public Key Enchamism (PKE) is a quadruple of algorithms and a corresponding key space , a ciphertext space with
- The parameter generation algorithm takes input , where is the security parameter and return global parameter .
- The key generation algorithm takes input param and returns a public and secret-key pair ().
- The encryption algorithm takes and a message and returns a ciphertext .
- The deterministic decryption algorithm takes and returns a message , with denoting as a failure.