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The authors construct an efficient identity based encryption system based on the standard Learning With Errors (LWE) problem. Their security proof holds in the standard model. The key step in the construction is a family of lattices for which there are two distinct trapdoors for finding short vectors. One trapdoor enables the real system to generate short vectors in all lattices in the family. The other trapdoor enables the simulator to generate short vectors for all lattices in the family except for one. They extend this basic technique to an adaptively-secure IBE and a Hierarchical IBE.
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