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arXiv · 2606.16146

When Proofs Meet Hardware: Comparing NTT and SumCheck in Zero-Knowledge Systems

Jianqiao Mo·Alhad Daftardar·Barath GaneshKumar·Kaiyue Guo·Hong Wang·Benedikt Bunz·Siddharth Garg·Brandon Reagen
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Abstract

In the ZKP community, it has long been discussed that the SumCheck protocol is asymptotically more efficient than the Number Theoretic Transform (NTT), requiring only $O(N)$ arithmetic versus $O(N \log N)$. At the same time, hardware accelerator designers propose that NTT is more hardware-friendly, benefiting from locality and data reuse, while SumCheck suffers from sequential, dependent rounds. Despite these competing intuitions, the hardware-system-level trade-offs between NTT- and SumCheck-based proving primitives remain insufficiently understood. Beyond individual accelerator design, this work presents, to our knowledge, the first hardware-system-level direct comparison of NTT- and SumCheck-based proving primitives under a unified architectural framework. We study them in the context of the ZeroCheck protocol, a common building block in zkSNARKs. We implement optimized systems for both primitives. Both are evaluated under the same level on-chip SRAM and off-chip bandwidth budgets. Our results show that there is no universal winner. Generally, SumCheck outperforms NTT for high-degree polynomials. For low-degree polynomials, performance depends on memory availability: under given SRAM budgets, NTT might deliver better performance for medium-sized workloads by exploiting data reuse. These findings, bridging cryptographic protocol design and hardware architecture, offer practical guidance for understanding the proving cost of NTT- and SumCheck-based zero-knowledge proof systems.

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Jianqiao Mo, Alhad Daftardar, Barath GaneshKumar, Kaiyue Guo, Hong Wang, Benedikt Bunz, Siddharth Garg, Brandon Reagen. 2026-06-15. When Proofs Meet Hardware: Comparing NTT and SumCheck in Zero-Knowledge Systems. https://arxiv.org/abs/2606.16146

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