Variants of this definition define indistinguishability under chosen ciphertext attack and adaptive chosen ciphertext attack (IND-CCA, IND-CCA2).
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Unlike other security definitions, semantic security does not consider the case of chosen ciphertext attack (CCA), where an attacker is able to request the decryption of chosen ciphertexts, and many semantically secure encryption schemes are demonstrably insecure against chosen ciphertext attack.
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An early example of such requirements and proof was given by Goldwasser and Micali for semantic security and the construction based on the quadratic residuosity problem.