Fully-Secure Lattice-Based IBE as Compact as PKE

We construct an identity-based encryption (IBE) scheme from the standard Learning with Errors (LWE) assumption, which both has a compact public-key (with size similar to known lattice-based PKE schemes) and also achieves adaptive security in the standard model. This improves over previous IBE schemes from lattices, which either have a public key that grows at least linearly with the length of the supported identities, or achieve a non-adaptive notion of security, or require a random oracle. Additionally, our techniques from IBE can be adapted to construct a compact digital signature scheme, which achieves existential unforgeability under the standard Short Integer Solution (SIS) assumption with small polynomial parameters.