zkDaily - 2026-03-21

零知识证明 zkDaily

ZKP Frontier Tracker 🎯

Sat

03.21

2026

S-two Whitepaper

Paper

https://eprint.iacr.org/2026/532

Dan Carmon Circle STARK Flat AIR

Carmon et al. proposed S-two, a circle STARK over the Mersenne prime field, formalizing the flat AIR circuit model and providing in-depth security analysis of proof of proximity, highlighting cross-domain correlated agreement.

Notes

S-two is a circle STARK implementation over the Mersenne prime field (modulus p=2^31-1)
Formalizes the flat AIR circuit model used by modern ZK virtual machines
Provides in-depth security analysis of proof of proximity for flat AIRs
Highlights importance of cross-domain correlated agreement for multi-table proofs
Shows multi-table circle FRI satisfies this notion up to Johnson bound
Discusses conjectures on list-decodability and line-decodability of Reed-Solomon codes

Collected by @icerdesign

零知识证明 zkDaily

Q&A Deep Dive 💬

Sat

03.21

2026

What is S-two and how does it differ from traditional STARKs?

S-two is a circle STARK-based proof system over a Mersenne prime field. Compared to traditional STARKs, it uses flat AIR and multi-table structures, improving proof of proximity efficiency for zkVMs.

Why do multi-table designs introduce soundness challenges?

Multi-table designs split constraints across traces, risking inconsistency and increasing soundness error. S-two introduces cross-domain correlated agreement to enforce consistency, combined with batch evaluation to maintain correctness.

How does cross-domain correlated agreement reduce soundness error?

It enforces consistency across functions over different domains, restricting adversarial solutions. Combined with circle FRI, it achieves soundness close to the Johnson bound of Reed-Solomon codes, controlling errors in multi-table proofs.

Prompted by @icerdesign