In cryptography, a cryptosystem is semantically secure if any probabilistic, polynomial-time algorithm (PPTA) that is given the ciphertext of a certain message (taken from any distribution of messages), and the message's length, cannot determine any partial information on the message with probability non-negligibly higher than all other PPTA's that only have access to the message length (and not the ciphertext). In other words, knowledge of the ciphertext (and length) of some unknown message does not reveal any additional information on the message that can be feasibly extracted. This concept is the computational complexity analogue to Shannon's concept of perfect secrecy. Perfect secrecy means that the ciphertext reveals no information at all about the plaintext, whereas semantic security implies that any information revealed cannot be feasibly extracted.
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Some articles on semantic security:
... Under sufficiently strong security guarantees the attacks proposed above become infeasible, as the adversary will be unable to correlate any two encryptions of the same message ... This guarantee is known as semantic security or indistinguishability, and has several definitions depending on the assumed capabilities of the attacker (see semantic security) ... it is important to understand what is the maximum level of security that can be guaranteed ...
... The original cryptosystem as shown above does provide semantic security against chosen-plaintext attacks (IND-CPA) ... malleable, and therefore does not enjoy the highest echelon of semantic security that protects against adaptive chosen-ciphertext attacks (IND-CCA2) ...
... Semantic security considers only the case of a "passive" attacker, i.e ... 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 ... Consequently, semantic security is now considered an insufficient condition for securing a general-purpose encryption scheme ...
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