Public Key Broadcast Encryption with Low Number of Keys and Constant Decryption Time (Version 2)

In this paper we propose two public key BE schemes that have efficient complexity measures. The first scheme, called the PBE-PI scheme, has $O(r)$ header size, $O(1)$ public keys and $O(\log N)$ private keys per user, where $r$ is the number of revoked users. This is the first public key BE scheme that has both public and private keys under $O(\log N)$ while the header size is $O(r)$. These complexity measures match those of efficient secret key BE schemes. \par Our second scheme, called the PBE-SD-PI scheme, has $O(r)$ header size, $O(1)$ public key and $O(\log N)$ private keys per user also. However, its decryption time is remarkably $O(1)$. This is the first public key BE scheme that has $O(1)$ decryption time while other complexity measures are kept low. Overall, this is the most efficient public key BE scheme up to now. \par Our basic schemes are one-way secure against {\em full collusion of revoked users} in the random oracle model under the BDH assumption. We modify our schemes to have indistinguishably security against adaptive chosen ciphertext attacks