On the security notions of signcryption

Libert and Quisquater introduced several strong security notions of signcryptions. Recently, Wang, Manulis, Au and Susilo investigated the relationships among them and showed the key invisibility is the strongest one in a sense that the key invisibility implies the other notions. In this paper, we revisit the WMAS's results. We introduce an intermediate notion called the weak key invisibility and show that the combination of the indistinguishability and the ciphertext anonymity implies the weak key invisibility. We also give a condition so that the weak key invisibility is equivalent to the key invisibility.