This work package will pursue two main objectives: extending the reaches of practical lattice-based cryptography and exploring novel constructions with functionalities that are not currently present in any (not necessarily lattice-based) primitive. There are currently very efficient basic primitives such as public-key encryption, identity-based encryption, and digital signatures, but there is a surprising road-block when trying to construct practical, more advanced primitives. We believe that, by the end of this project, the results of this work package will greatly expand the toolbox of efficient, advanced lattice cryptography.
Throughout the work package, we will not merely try to translate the number-theoretic constructions into lattice-based ones, as this approach may not result in efficient constructions. We will also attempt to illuminate which types of constructions can be efficiently built from lattices, and then attempt to design the protocols in work packages 5 and 6 based on these new efficient building blocks. In this manner, we believe that by the end of the project, we will have novel protocol designs that are based on the types of basic building blocks that can be built efficiently from lattices.