Adaptive Security of Broadcast Encryption, Revisited

We provide a strong security notion for broadcast encryption, called adaptive security in the multichallenge setting (MA-security), where the adversary can adaptively have access to the key generation oracle and the encryption oracle many times (multichallenge). The adversary specially can query for the challenge ciphertexts on different target user sets adaptively, which generalizes the attacks against broadcast encryptions in the real world setting. Our general result shows that the reduction of the adaptive secure broadcast encryption will lose a factor of in the MA setting, where is the maximum number of encryption queries. In order to construct tighter MA-secure broadcast encryptions, we investigate Gentry and Water's transformation and show that their transformation can preserve MA-security at the price of reduction loss on the advantage of the underlying symmetric key encryption. Furthermore, we remove the -type assumption in Gentry and Water's semistatically secure broadcast encryption by using Hofheinz-Koch-Striecks techniques. The resulting scheme instantiated in a composite order group is MA-secure with constant-size ciphertext header.

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