Efficient NIZKs and Signatures from Commit-and-Open Protocols in the QROM

TL;DR

This paper proves tight online extractability of commit-and-open Sigma-protocols in the quantum random oracle model, enhancing the post-quantum security of digital signatures like Picnic using classical reasoning frameworks.

Contribution

It extends the security proofs of commit-and-open protocols to the QROM, supporting post-quantum security with both hash-based and Merkle-tree commitments.

Findings

Proves tight online extractability in the QROM for hash-based commitments.

Extends results to Merkle-tree based commitments.

Improves provable post-quantum security of the Picnic signature scheme.

Abstract

Commit-and-open Sigma-protocols are a popular class of protocols for constructing non-interactive zero-knowledge arguments and digital-signature schemes via the Fiat-Shamir transformation. Instantiated with hash-based commitments, the resulting non-interactive schemes enjoy tight online-extractability in the random oracle model. Online extractability improves the tightness of security proofs for the resulting digital-signature schemes by avoiding lossy rewinding or forking-lemma based extraction. In this work, we prove tight online extractability in the quantum random oracle model (QROM), showing that the construction supports post-quantum security. First, we consider the default case where committing is done by element-wise hashing. In a second part, we extend our result to Merkle-tree based commitments. Our results yield a significant improvement of the provable post-quantum security of the digital-signature scheme Picnic. Our analysis makes use of a recent framework by Chung et al. [arXiv:2010.11658] for analysing quantum algorithms in the QROM using purely classical reasoning. Therefore, our results can to a large extent be understood and verified without prior knowledge of quantum information science.