zkDaily - 2026-03-12

零知识证明 zkDaily

ZKP Frontier Tracker 🎯

Thu

03.12

2026

Lookup Arguments over Rings and Applications to Batch-Verification of RAM Programs

Paper

https://eprint.iacr.org/2026/471

Jonathan Bootle Rings

Bootle et al. proposed ring-based lookup arguments in their paper, extending Plookup and LogUp protocols for batch verification of RAM programs, addressing compatibility in post-quantum schemes.

Notes

Existing lookup arguments are field-based, incompatible with ring-based post-quantum lattice schemes.
Systematic security issues arise when translating field techniques to rings; some known arguments are vulnerable.
Extend Plookup and LogUp polynomial IOPs to ring R=Zq[X]/(Xd+1).
Combine with lattice-based polynomial commitments for succinct lattice-based lookup arguments.
Apply ring lookups for batch verification of RAM updates with arbitrary ring elements.
Provides key components for post-quantum ZK systems, improving efficiency for arithmetization-unfriendly operations.

Collected by @icerdesign

零知识证明 zkDaily

Q&A Deep Dive 💬

Thu

03.12

2026

Why study lookup arguments over rings?

Most existing lookup arguments are designed over finite fields. However, many post quantum cryptographic systems, especially lattice based ones, operate over rings. Studying lookup arguments over rings allows SNARK systems to work with these post quantum constructions.

Why can translating lookup arguments from fields to rings cause problems?

In fields, algebraic properties ensure certain polynomial identities behave predictably. Rings may contain different structures, such as zero divisors, which break assumptions used in field based protocols. The paper shows that some known lookup constructions become insecure when directly applied to rings.

How are ring based lookup arguments combined with lattice polynomial commitments?

The protocol first constructs lookup relations as a polynomial IOP over the ring. Polynomial commitments based on lattice assumptions are then used to commit to and verify the polynomials. This produces succinct proofs while maintaining post quantum security.

Prompted by @icerdesign