Adaptively secure broadcast encryption under standard assumptions with better efficiency

In this paper, we present an efficient public-key broadcast encryption (PKBE) scheme with sublinear size of public keys, private keys, and ciphertexts and prove its adaptive security under standard assumptions. Compared with the currently best scheme that provides adaptive security under standard assumptions and sub-linear size of various parameters, the ciphertext size of our scheme is 94% shorter and the encryption algorithm of our scheme is also 2.8 times faster than those of the currently best scheme. To achieve our scheme, we adapt the dual system encryption technique of Waters. However, there is a challenging problem to use this technique for the construction of PKBE with sub-linear size of ciphertexts such as a tag compression problem. To overcome this problem, we first devise a novel tag update technique for broadcast encryption. Using this technique, we build an efficient PKBE scheme in symmetric bilinear groups, and prove its adaptive security under standard assumptions. After that, we build another PKBE scheme in asymmetric bilinear groups and also prove its adaptive security under simple assumptions.