Bonsai Trees (or, Arboriculture in Lattice-Based Cryptography)

We introduce bonsai trees, a lattice-based cryptographic primitive that we apply to resolve some important open problems in the area. Applications of bonsai trees include: • An efficient, stateless ‘hash-and-sign’ signature scheme in the standard model (i.e., no random oracles), and • The first hierarchical identity-based encryption (HIBE) scheme (also in the standard model) that does not rely on bilinear pairings. Interestingly, the abstract properties of bonsai trees seem to have no known realization in conventional number-theoretic cryptography.