On the security of the identity-based encryption based on DHIES from ASIACCS 2010

In ASIACCS 2010, Chen, Charlemagne, Guan, Hu and Chen proposed an interesting construction of identity-based encryption based on DHIES, whose key extraction algorithm makes use of the multivariate quadratic equation. They proved that their scheme is selective-ID secure against chosen ciphertext attack, i.e. secure in the sense of IND-sID-CCA. Unfortunately, in this paper, we demonstrate that Chen et al.'s scheme is insecure in the sense of IND-sID-CCA by showing that the private key extraction algorithm of their scheme can be exploited to apply XL algorithm, which is to solve the multivariate quadratic (MQ) problem (under certain conditions).