The Groth-Sahai proof system is a highly efficient pairing-based proof system for a specific class of group-based languages. Cryptographic primitives that are compatible with these languages (such that we can express, e.g., that a ciphertext contains a valid signature for a given message) are called “structure-preserving”. The combination of structure-preserving primitives with Groth-Sahai proofs allows to prove complex statements that involve encryptions and signatures, and has proved useful in a variety of applications. However, so far, the concept of structure-preserving cryptography has been confined to the pairing setting.
In this talk, I will outline a strategy for structure-preserving cryptography from lattices. At the heart of this framework lies a lattice-based argument system for “noisy” languages (formalized as “structure-preserving sets”), and the observation that this proof system is compatible with a number of existing lattice-based primitives. We demonstrate the usefulness of our framework with a lattice-based construction of verifiably encrypted signatures. As a secondary contribution, we present a more efficient variant of Rückert's signature scheme. I should note that (like in the group-based setting of structure-preserving cryptography), all our constructions are in the standard model.
Before joining ETH Zurich's CS department in 2020, I used to work at the Karlsruhe Institute of Technology in Germany, and before that at the Centrum Wiskunde en Informatica in Amsterdam, the Netherlands. I work on the foundations of cryptography, and in particular on the design and analysis of cryptographic building blocks (such as public-key encryption and signatures).