KDM and Selective Opening Secure IBE Based on the LWE Problem
Jingnan He, Bao Li, Xianhui Lu, Dingding Jia, Wenpan Jing · 2017
Based on the learning with errors (LWE) problem, we construct an identity-based encryption (IBE) scheme in the standard-model which is secure against the key dependent message (KDM) attacks and the selective opening (SO) attacks. KDM security, which requires that the scheme can still obtain secrecy even if the messages depend on the secret key, is necessary for IBE when updating the identity secret keys with the old ones. SO security, which requires that when the adversary corrupts some fraction of senders, the uncorrupted senders' messages still maintain privacy, is useful for IBE since that one user receives messages from many senders is a natural scenario. Although there is a KDM secure IBE scheme based on LWE constructed by Alperin-Sheriff and Peikert (PKC'12), and a SO secure IBE scheme based on LWE constructed by He et al. (IWSEC'15), those two schemes cannot achieve both of the security requirements at the same time.