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

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

零知识证明 zkDaily

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