The concept of identity-based cryptosystem was introduced by Adi Shamir in 1984. In this
new paradigm users' public key can be any string which uniquely identifies the user. The
task of Public Key Generator (PKG) in IBE is to authenticate identity of the entity, generate
the private key corresponding to the identity of the entity and finally transmit the private key
securely to the entity. In large network PKG has a burdensome job. So the notion of
Hierarchical IBE (HIBE) was introduced in [11, 12] to distribute the workload by delegating …

We construct an efficient identity based encryption system based on the standard learning
with errors (LWE) problem. Our 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. We extend this basic technique to an adaptively-secure IBE and …