Adaptively secure identity‐based broadcast encryption with constant size private keys and ciphertexts from the subgroups

The main challenge in building efficient broadcast systems is to encrypt messages with short ciphertexts. The well‐known constructions of identity‐based broadcast encryption (IBBE) 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. These folklore construction methods lead to schemes that are somewhat inefficient and leave open the problem of finding more efficient direct constructions. In this paper, we give a secure identity‐based broadcast encryption scheme with a constant‐size ciphertext and private keys. It is constructed by using dual techniques in the subgroups. The proposed scheme achieves the full security (adaptive security) under three static (i.e. non $q$ ‐based) assumptions. It is worth noting that only recently Waters’s scheme achieves adaptive security under simple assumptions. One feature of our scheme is that it is relatively simple to get adaptive security.