Welcome to the resource topic for 2022/1545
Title:
On Structure-Preserving Cryptography and Lattices
Authors: Dennis Hofheinz, Kristina Hostakova, Roman Langrehr, Bogdan Ursu
Abstract: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 work, we propose the first framework for structure-preserving cryptography in the lattice setting. Concretely, we
- define “structure-preserving sets” as an abstraction of (typically noisy) lattice-based languages,
- formalize a notion of generalized structure-preserving encryption and signature schemes capturing a number of existing lattice-based encryption and signature schemes),
- construct a compatible zero-knowledge argument system that allows to argue about lattice-based structure-preserving primitives,
- offer a lattice-based construction of verifiably encrypted signatures in our framework. Along the way, we also discover a new and efficient strongly secure lattice-based signature scheme. This scheme combines Rückert’s lattice-based signature scheme with the lattice delegation strategy of Agrawal et al., which yields more compact and efficient signatures.
We hope that our framework provides a first step towards a modular and versatile treatment of cryptographic primitives in the lattice setting.
ePrint: https://eprint.iacr.org/2022/1545
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