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The authors present efficient Identity-Based Encryption (IBE) and signature schemes under the Symmetric eXternal Diffie-Hellman (SXDH) assumption in bilinear groups. 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. Their constructions use both dual system encryption (Waters, Crypto '09) and dual pairing vector spaces (Okamoto and Takashima, Pairing '08, Asiacrypt '09). Specifically, they show how to adapt the recent DLIN-based instantiations of Lewko (Eurocrypt '12) to the SXDH assumption. To their knowledge, this is the first work to instantiate either dual system encryption or dual pairing vector spaces under the SXDH assumption.
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