Toward 3-Constant Size Identity Based Broadcast Encryption Based on Proxy Re-Encryption

3-Constant size identity based broadcast encryption means identity based broadcast encryption with constant size ciphertext, public key and private key. Identity based broadcast encryption schemes enable senders to efficiently broadcast ciphertexts to a large set of receivers in a way that only non-revoked receivers can decrypt them. Until now, the best broadcast encryption can only achieve $O(n)$-size public key, constant size ciphertext and constant size private key or $O(\sqrt{n})$-size public key, $O(\sqrt{n})$-size ciphertexts and constant size private key, which proposed by Boneh, Gentry and Waters in Eurocrypt'05. Naturally, we ask this question: can we construct constant size ciphertext, public key and private key broadcast encryption? It seems very difficult to gain this result. However, when we considering identity based broadcast encryption, this result can be gained. In particular, in this paper we show how to construct 3-constant size identity based broadcast encryption based on identity based proxy re-encryption with the help PKG.