Identity-Based Encryption in DDH Hard Groups

The concept of Identity-Based Encryption was first introduced by Shamir (CRYPTO 1984) but were not realised until much later Sakai, Ohgishi and Kasahara (SCIS 2000), Boneh Franklin 2001) Cocks (IMACC 2001). Since then, has been a highly active area research. While there have several instantiations its variants, is one glaring omission: no in plain Decisional Diffie-Hellman groups. This seemed at odds with the fact that we can instantiate almost every single cryptographic primitive An answer to this question came result Papakonstantinou, Rackoff Vahlis (EPRINT 2012), who showed it impossible an DDH impossibility questioned when Döttling Garg 2017) presented based on problem. However, did disprove result, as requires use garbled circuits, which are inherently interactive. type scheme covered does raise some questions. In paper, those questions constructing We achieve instantiating generic construction Witness Garg, Gentry, Sahai Waters (STOC 2013), minor changes. To end, construct unique signature groups, best our knowledge. scheme, inefficient, unavoidable. Our completely contradict instead shows statement too strong, only rules out efficient constructions.