Compact Identity Based Encryption from LWE

We construct an identity-based encryption (IBE) scheme from the standard Learning with Errors (LWE) assumption that has compact public-key and achieves adaptive security in the standard model. In particular, our scheme only needs 2 public matrices to support O(log λ)-bit length identity, and O(λ/ log λ) public matrices to support λ-bit length identity. This improves over previous IBE schemes from lattices substantially. 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.