Lattice-Based zk-SNARKs from Square Span Programs

Rosario Gennaro (1) , Michele Minelli (2, 3, 4) , Anca Nitulescu (3, 2, 4) , Michele Orrù (4, 3, 2)

1 IBM Watson Research Center
2 PSL - Université Paris Sciences et Lettres
3 DI-ENS - Département d'informatique - ENS Paris
4 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities

Zero-knowledge SNARKs (zk-SNARKs) are non-interactive proof systems with short (i.e., independent of the size of the witness) and efficiently verifiable proofs. They elegantly resolve the juxtaposition of individual privacy and public trust, by providing an efficient way of demonstrating knowledge of secret information without actually revealing it. To this day, zk-SNARKs are widely deployed all over the planet and are used to keep alive a system worth billion of euros, namely the cryptocurrency Zcash. However, all current SNARKs implementations rely on so-called pre-quantum assumptions and, for this reason, are not expected to withstand cryptanalitic efforts over the next few decades. In this work, we introduce a new zk-SNARK that can be instantiated from lattice-based assumptions, and which is thus believed to be post-quantum secure. We provide a generalization in the spirit of Gennaro et al. (Eurocrypt'13) to the SNARK of Danezis et al. (Asiacrypt'14) that is based on Square Span Programs (SSP) and relies on weaker computational assumptions. We focus on designated-verifier proofs and propose a protocol in which a proof consists of just 5 LWE encodings. We provide a concrete choice of parameters, showing that our construction is practically instantiable.

Mots clés: Post-quantum; Zero-knowledge; SNARK

Domaines: Cryptographie et sécurité [cs.CR]

Rosario Gennaro, Michele Minelli, Anca Nitulescu, Michele Orrù. Lattice-Based zk-SNARKs from Square Span Programs. ACM CCS 2018, Oct 2018, Toronto, Canada. ⟨hal-01743360⟩