International Association
for Cryptologic Research

We 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. 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.