Identity-based encryption in DDH hard groups

摘要: The concept of Identity-Based Encryption was first introduced by Shamir (CRYPTO 1984) but were not realised until much later by Sakai, Ohgishi and Kasahara (SCIS 2000), Boneh and Franklin (CRYPTO 2001) and Cocks (IMACC 2001). Since then, Identity-Based Encryption has been a highly active area of research. While there have been several instantiations of Identity-Based Encryption and its variants, there is one glaring omission: there have been no instantiations in plain Decisional Diffie-Hellman groups. This seemed at odds with the fact that we can instantiate almost every single cryptographic primitive in plain Decisional Diffie-Hellman groups. An answer to this question came in a result by Papakonstantinou, Rackoff and Vahlis (EPRINT 2012), who showed that it is impossible to instantiate an Identity-Based Encryption in plain DDH groups. The impossibility result was questioned when Döttling and Garg …