Public key encryption schemes supporting equality test with authorisation of different granularity

In this paper, we extended the work about public key encryption schemes supporting fine-grained authorization (FG-PKEET), done by Tang (2011b). First of all, we correct some flaws in Tang (2011b) and discuss how to extend the proposed cryptosystem to support approximate equality test. Secondly, we present a comparison between FG-PKEET and other similar primitives including AoN-PKEET by Tang (2011a) and PKEET by Yang et al. (2010), and demonstrate their differences in complexity and achieved security. Thirdly, to mitigate the inherent offline message recovery attacks, we extend FG-PKEET to a two-proxy setting, where two proxies need to collaborate in order to perform an equality test. Finally, we propose a cryptosystem and prove its security in the two-proxy setting.