Zinc: Succinct arguments with small arithmetization overheads from IOPs of proximity to the integers
Albert Garreta
Abstract:
We introduce Zinc, a hash-based succinct argument for integer arithmetic. Zinc's goal is to provide a practically efficient scheme that bypasses the arithmetization overheads that many succinct arguments present. These overheads can be of orders of magnitude in many applications. By enabling proving statements over the integers, we are able to arithmetize many operations of interest with almost no overhead. This includes modular operations involving any moduli, not necessarily prime, and possibly involving multiple moduli in the same statement. In particular, Zinc allows to prove statements for the ring Z/nZ for arbitrary n. Importantly, and departing from prior work, our schemes are purely code and hash-based, and do not require hidden order groups. In its final form, Zinc operates similarly to other hash-based schemes using Brakedown as their PCS, and at the same time it benefits from the arithmetization perks brought by working over the integers (and the rationals) natively. To build Zinc we introduce and instantiate a new primitive that enforces provers to use witnesses with all its entries "close" to being integers. Such primitive, which we call IOP of proximity to the integers, is analogous to an IOP of proximity to a linear code.
Bio:
Albert Garreta leads the cryptography research team at Nethermind, a role he has held since 2023. Previously, he was a postdoctoral fellow at the Basque Center for Applied Mathematics (Spain). He earned his PhD in mathematics from Stevens Institute of Technology (NJ, USA). His research focuses on various zk-related topics, including code-based SNARKs, lookup and folding schemes, and the soundness aspects of interactive proofs. He has coauthored several academic papers in both mathematics and cryptography. Selected works include: Zinc: Succinct arguments with small arithmetization overheads from IOPs of proximity to the integers (https://eprint.iacr.org/2025/316) Fiat-Shamir Security of FRI and Related SNARKs (Asiacrypt 2023) FLI: Folding Lookup Instances (Asiacrypt 2024) On Soundness Notions for Interactive Oracle Proofs (Journal of Cryptology)