Full Security: Fuzzy Identity Based Encryption

At EUROCRYPT 2005, Sahai and Waters presented the Fuzzy Identity Based Encryption (Fuzzy-IBE) which could be used for biometrics and attribute-based encryption in the selective-identity model. When a secure Fuzzy-IBE scheme in the selective-identity model is transformed to full identity model it exist an exponential loss of security. In this paper, we use the CPA secure Gentry's IBE (exponent inversion IBE) to construct the first Fuzzy IBE that is fully secure without random oracles. In addition, the same technique is used to the modification of CCA secure Gentry's IBE which introduced by Kiltz and Vahlis to get the CCA secure Fuzzy IBE in the full-identity model.