Improving the Message-Ciphertext Rate of Lewko's Fully Secure IBE Scheme

In Eurocrypt 2012, Lewko presented a fully secure IBE scheme in the prime order setting based on the decisional linear assumption. We note that some random factor involved in the ciphertext can further be used to hide yet another message , and get a new fully secure IBE scheme with better message-ciphertext rate. Similar to Lewko’s scheme, we use dual pairing vector space in prime order bilinear groups to simulate the canceling and parameter hiding properties of composite order settings. The security of our scheme is based on the subspace assumption, which can be reduced to the decisional linear assumption. We employ the dual system encryption technique in our security proof.