Functional encryption for threshold functions (or fuzzy IBE) from lattices Cryptosystems based on the hardness of lattice problems have recently acquired much importance due to their averagecase to worstcase equivalence, their conjectured resistance to quantum cryptanalysis, their ease of implementation and increasing practicality, and, lately, their promising potential as a platform for constructing advanced  :44,this work, we construct xe2x80x9cFuzzyxe2x80x9d Identity Based Encryption from the hardness of the Learning With Errors (LWE) problem. We note that for our parameters, the underlying lattice problems (such as gapSVP or SIVP) are assumed to be hard to approximate within supexponential factors for adversaries running in subexponential time. We give CPA and CCA secure variants of our construction, for small and large universes of attributes. All our constructions are secure against selectiveidentity attacks in the standard model. Our construction is made possible by observing certain special properties that secret sharing schemes need to satisfy in order to be useful for Fuzzy IBE. We also discuss some obstacles towards realizing latticebased attributebased encryption (ABE).

Implementation of a Strongly Robust IdentityBased Encryption Scheme over Type3 Pairings Identitybased encryption (IBE) is a powerful mechanism for maintaining security. However, systems based on IBE are unpopular when compared with those of the publickey encryption (PKE). In our opinion, one of the reasons is a gap between theory and practice. For example, a generic transformation of weaklystrongly robust IBE from any IBE has been proposed by Abdalla et al., no robust IBE scheme is explicitly given. This means that, theoretically, anyone can construct a weaklystrongly robust IBE scheme by employing this transformation. However, this seems not easily applicable to noncryptographers. In this paper, we first introduce the Gentry IBE scheme constructed over Type3 pairings by employing the transformation proposed by Abe et al., and second we explicitly give stronglyweakly robust Gentry IBE schemes by employing the Abdalla et al. transformation. Finally, we show its implementation result and show that we can add strong robustness to the Gentry IBE scheme with a very few additional costs. We employ the mcl library to support a BarretoNaehrig curve defined over the 462bit prime. The encryption requires about 9 ms, whereas the decryption requires about 12 ms.