Summary: We introduce a refined definition of semantic security. The new definition is valid against not only chosen-plaintext attacks but also chosen-ciphertext attacks whereas the original one is defined against only chosen-plaintext attacks. We show that semantic security formalized by the new definition is equivalent to indistinguishability, due to Goldwasser and Micali for each of chosen-plaintext attacks, non-adaptive chosen-ciphertext attack, and adaptive chosen-ciphertext attack.