Shorter IBE and Signatures via Asymmetric Pairings

We present efficient Identity-Based Encryption (IBE) and signature schemes under the Symmetric External Diffie-Hellman (SXDH) assumption in bilinear groups; our IBE scheme also achieves anonymity. In both the IBE and the signature schemes, all parameters have constant numbers of group elements, and are shorter than those of previous constructions based on Decisional Linear (DLIN) assumption. Our constructions use both dual system encryption (Waters, Crypto ’09) and dual pairing vector spaces (Okamoto and Takashima, Pairing ’08, Asiacrypt ’09). Specifically, we show how to adapt the recent DLIN-based instantiations of Lewko (Eurocrypt ’12) to the SXDH assumption. To our knowledge, this is the first work to instantiate either dual system encryption or dual pairing vector spaces under the SXDH assumption. Furthermore, our work could be extended to many other Functional Encryption. Particularly, we show how to instantiate our framework to Inner Product Encryption (IPE) and Key-Policy Functional Encryption (KP-FE). All parameters of our constructions are shorter than those of DLIN-based constructions. ⋆ Research of the authors is supported in part by the National Research Foundation of Singapore under Research Grant NRF-CRP2-2007-03. Hoeteck Wee’s work is also supported by NSF CAREER Award CNS-1237429.