An asymmetric, i.e. public-key, encryption scheme allows a sender to use a recipient's public key to transmit an encryption of a message to the receiver, who can use his secret key to decrypt the given ciphertext, thereby obtaining the original message.
Such a scheme should be secure in the sense that no information about the message should be leaked to a (resource-bounded) attacker, even if that attacker mounts a so-called 'chosen ciphertext' attack, in which he may obtain decryptions of other ciphertexts. This is the strongest type of attack that has been proposed for a public-key encryption scheme.
ISO/IEC 18033-2:2006 specifies the functional interface of such a scheme, and in addition specifies a number of particular schemes that appear to be secure against chosen ciphertext attack. The different schemes offer different trade-offs between security properties and efficiency.