The LaZer Library: Lattice-Based Zero Knowledge and Succinct Proofs for Quantum-Safe Privacy

Abstract

The hardness of lattice problems offers one of the most promising security foundations for quantum-safe cryptography. Basic schemes for public key encryption and digital signatures are already close to standardization at NIST and several other standardization bodies, and the research frontier has moved on to building primitives with more advanced privacy features. At the core of many such primitives are zero-knowledge proofs. In recent years, zero-knowledge proofs for (and using) lattice relations have seen a dramatic jump in efficiency and they currently provide arguably the shortest, and most computationally efficient, quantum-safe proofs for many scenarios. The main difficulty in using these proofs by non-experts (and experts!) is that they have a lot of moving parts and a lot of internal parameters depend on the particular instance that one is trying to prove. Our main contribution is a library for zero-knowledge and succinct proofs which consists of efficient and flexible C code underneath a simple-to-use Python interface. Users without any background in lattice-based proofs should be able to specify the lattice relations and the norm bounds that they would like to prove and the library will automatically create a proof system, complete with the intrinsic parameters, using either the succinct proofs of LaBRADOR (Beullens and Seiler, Crypto 2023) or the linear-size, though smaller for certain application, proofs of Lyubashevsky et al. (Crypto 2022). The Python interface also allows for common operations used in lattice-based cryptography which will enable users to write and prototype their full protocols within the syntactically simple Python environment. We showcase some of the library's usefulness by giving protocol implementations for blind signatures, anonymous credentials, the zero-knowledge proof needed in the recent Swoosh protocol (Gajland et al., Usenix 2024), proving knowledge of Kyber keys, and an aggregate signature scheme. Most of these are the most efficient, from a size, speed, and memory perspective, known quantum-safe instantiations.