Straight-Line Knowledge Extraction for Multi-Round Protocols

The Fiat-Shamir (FS) transform is the standard approach to compiling interactive proofs into non-interactive ones. However, the fact that knowledge extraction typically requires rewinding limits its applicability without having to rely on further heuristic conjectures. A better alternative is a transform that guarantees straight-line knowledge extraction. Two such transforms were given by Pass (CRYPTO '03) and Fischlin (CRYPTO '05), respectively, with the latter giving the most practical parameters. Pass's approach, which is based on cut-and-choose, was also adapted by Unruh (EUROCRYPT '12, '14, '15) to the quantum setting, where rewinding poses a different set of challenges. All of these transforms are tailored at the case of three-round Sigma protocols, and do not apply to a number of popular paradigms for building succinct proofs (e.g., those based on folding or sumcheck) which rely on multi-round protocols.

This work initiates the study of transforms with straight-line knowledge extraction for multi-round protocols. We give two transforms, which can be thought of as multi-round analogues of those by Fischlin and Pass. Our first transform leads to more efficient proofs, but its usage applies to a smaller class of protocols than the latter one. Our second transform also admits a proof of security in the Quantum Random Oracle Model (QROM), making it the first transform for multi-round protocols which does not incur the super-polynomial security loss affecting the existing QROM analysis of the FS transform (Don et al., CRYPTO '20).