摘要：How to build an efficient identity-based broadcast system with short ciphertexts is a main challenge at present. The existing constructions with constant size ciphertexts in the standard model are based on the non-standard cryptography assumption. In addition, these constructions cannot solve the trade-off between the private keys and ciphertexts. Hence these methods lead to schemes that are somewhat inefficient in the real world. To overcome these shortcomings, two schemes are introduced at first. The initial construction has constant size ciphertexts and O(| S |)-size private keys(where S denotes the set of receivers). Then the second scheme achieves constant size ciphertexts and constant size private keys which solve the trade-off between the private keys and ciphertexts. Furthermore, their security rests on the hardness of the decision Diffie-Hellman Exponent problem instead of other strong assumptions. However, both schemes only achieve a weak security-selective-identity security. Finally, two helpful constructions are proposed. They are constructed in the standard model and achieve full security which is stronger than selective-identity security.
