zkDaily - 2026-02-25

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ZKP Frontier Tracker 🎯

Wed

02.25

2026

Relaxed Modular PCS from Arbitrary PCS and Applications to SNARKs for Integers

Paper

https://eprint.iacr.org/2026/347

Alireza Shirzad Integer Arithmetic

Shirzad et al. proposed a black-box transformation from any PCS to relaxed modular PCS in their paper, applied to integer SNARKs, achieving the first fully succinct proof scheme for integer constraint systems.

Notes Notes 要点

Proposed black-box transformation from any PCS to relaxed modular PCS, extending existing techniques
Instantiated with tensor-code PCS for O(log(N+B)) proof size and verification time, transparent and post-quantum secure
Applied in Garetta et al. framework to achieve first fully succinct SNARK for integer customizable constraint systems
Prover time O(BlogN + NlogNlogB), verifier time and proof size O(log(N+B))
Used commitment-switching technique for integer polynomials and new batched integer commitment scheme
Improved arguments for integer addition, multiplication, NTT correctness, and Diophantine relations

Collected by @icerdesign

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Q&A Deep Dive 💬

Wed

02.25

2026

Why is direct support for integer arithmetic important for SNARKs?

Many applications natively operate over large integers, such as cryptographic protocols or number-theoretic computations. Avoiding emulation in finite fields reduces overhead and complexity.

Why are customizable constraint systems more challenging over integers?

Integer arithmetic lacks convenient finite-field properties such as guaranteed inverses and modular structure, making consistency and range enforcement harder to verify efficiently.

What does this result imply for the long-term development of SNARKs over integers?

It overturns the implicit belief that integer SNARKs cannot be both succinct and efficient, offering a transparent and plausibly post-quantum-secure path for large-integer cryptographic and number-theoretic applications.

Prompted by @icerdesign