pith. sign in

arxiv: 2606.03046 · v1 · pith:JHESJVFMnew · submitted 2026-06-02 · 💻 cs.AR · cs.CR

ZK-Flex: A Flexible and Scalable Framework for Accelerating Zero-Knowledge Proofs

Adiwena Putra , Cuong Manh Duong , Anh Quang Pham , Joo-Young Kim This is my paper

Pith reviewed 2026-06-28 08:26 UTC · model grok-4.3

classification 💻 cs.AR cs.CR
keywords zero-knowledge proofshardware accelerationToom-Cook multiplicationreconfigurable acceleratorspolynomial operationselliptic curve operationsnetwork on chiparea efficiency
0
0 comments X

The pith

ZK-Flex accelerates ZKP generation 5 to 11 times with up to 3.8 times better area efficiency.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces ZK-Flex to address the compute intensity of zero-knowledge proof generation, which is dominated by polynomial and elliptic-curve operations. These operations require support for large-precision modular multiplications and high hardware utilization as workloads shift between the two stages. The framework uses software optimizers for algorithmic choices and hardware with a Toom-Cook based core, flexible network on chip, and linked-list memory to improve parallelism. This co-design leads to substantial speedups and efficiency gains over existing accelerators.

Core claim

The central discovery is that a software-hardware co-designed framework called ZK-Flex, incorporating POLY and EC optimizers along with TCore—a Toom-Cook-based multi-precision core equipped with a flexible NoC and linked-list memory mechanism—can achieve 5 to 11 times speedup and up to 3.8 times higher area efficiency over the state of the art in representative ZKP benchmarks.

What carries the argument

TCore, the Toom-Cook-based multi-precision core with flexible NoC and linked-list memory mechanism, which supports diverse large-precision modular multiplications and maintains high utilization across shifting POLY and EC workloads.

If this is right

  • Reconfigurable accelerators can maintain high utilization as ZKP workloads shift between POLY and EC stages.
  • Software algorithmic choices tailored to hardware features can reduce overall computation in proof generation.
  • Limited memory capacity no longer constrains parallelism when using linked-list mechanisms in multi-precision cores.
  • Area efficiency gains make larger-scale ZKP deployments more feasible in resource-constrained settings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The flexible NoC and linked-list approach could extend to accelerators for other cryptographic workloads with variable precision needs.
  • Combining such hardware with emerging ZKP variants might require new optimizer layers but could preserve the reported efficiency ratios.
  • The reported speedups suggest potential for real-time ZKP use in systems where current accelerators fall short on throughput.

Load-bearing premise

That the TCore with Toom-Cook multiplication, flexible NoC, and linked-list memory mechanism can be implemented in hardware while maintaining high utilization across dynamically shifting POLY and EC workloads without significant unforeseen overheads or bottlenecks.

What would settle it

A hardware implementation or cycle-accurate simulation of ZK-Flex on the representative ZKP benchmarks that measures less than 5 times speedup or lower than 3.8 times area efficiency over the state of the art would falsify the claims.

Figures

Figures reproduced from arXiv: 2606.03046 by Adiwena Putra, Anh Quang Pham, Cuong Manh Duong, Joo-Young Kim.

Figure 1
Figure 1. Figure 1: Overview of the Groth16 ZKP protocol. 1 Introduction A Zero-Knowledge Proofs (ZKP) is a cryptographic protocol that allows a prover to convince a verifier of a statement’s correctness without revealing any secret information [8]. The resulting proof can be verified much more efficiently than re-executing the original computation. A typical use case is outsourcing, where a trusted but resource-limited clien… view at source ↗
Figure 3
Figure 3. Figure 3: (a-c) Various implementations for multi-precision multi [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Overview of the ZK-Flex framework. The software stack on the host CPU optimizes and generates instructions for the hardware, [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Toom–Cook multiplication [10], (b) Montgomery multi￾plier, and (c) configurable PEs for multi-precision modmul. {2, 3, 5, 7} instead of the next power of two. For example, with 33 constraints, the NP2 strategy pads to 64 (2 6 ), whereas NSC pads to 35 (5 × 7), reducing the number of MSM points from 64 to 35. The optimizer precomputes an NSC lookup table containing smooth composite numbers to efficientl… view at source ↗
Figure 7
Figure 7. Figure 7: (a) Linked-list memory chains point addresses within each [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Evaluation of ZK-Flex: (a) Mixed-radix NTT runtime across composite sizes. (b) Radix-2 NTT and MSM speedup over LegoZK. (c) [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
read the original abstract

Zero-knowledge proofs (ZKP) allows a prover to convince a verifier of computational correctness without revealing private data, ensuring both privacy and verifiability. However, proof generation is highly compute-intensive, dominated by polynomial (POLY) and elliptic-curve (EC) operations. These workloads pose two key challenges for hardware acceleration: (1) efficiently supporting diverse large-precision modular multiplications, and (2) maintaining high utilization across workloads that dynamically shift between POLY and EC stages. Existing reconfigurable accelerators address these issues only partially, remaining limited in precision scalability, algorithmic flexibility, and resource efficiency. To overcome these limitations, we propose ZK-Flex, a flexible and scalable software-hardware co-designed framework for accelerating ZKP proof generation. The software layer incorporates POLY and EC optimizers that reduce computation through hardware- and workload-aware algorithmic choices, while the hardware integrates TCore, a Toom-Cook-based multi-precision core with a flexible NoC and a linked-list memory mechanism that improves parallelism under limited memory capacity. Across representative ZKP benchmarks, ZK-Flex achieves 5 to 11 times speedup and up to 3.8 times higher area efficiency over the state of the art, establishing a new foundation for high-performance, reconfigurable ZKP acceleration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript presents ZK-Flex, a software-hardware co-designed framework for accelerating zero-knowledge proof generation. The software layer includes POLY and EC optimizers that make hardware- and workload-aware algorithmic choices. The hardware integrates TCore, a Toom-Cook-based multi-precision core, together with a flexible NoC and linked-list memory mechanism intended to improve parallelism under limited memory capacity. The central claim is that, across representative ZKP benchmarks, ZK-Flex delivers 5–11× speedup and up to 3.8× higher area efficiency relative to prior accelerators.

Significance. If the performance and efficiency numbers are substantiated by detailed, reproducible benchmarks, the work would address two recognized bottlenecks in ZKP hardware acceleration—support for diverse large-precision modular multiplications and sustained utilization across dynamically shifting POLY/EC workloads—thereby providing a concrete foundation for reconfigurable accelerators in this domain.

major comments (1)
  1. Abstract: the central performance claims (5–11× speedup and up to 3.8× area efficiency) are stated without any accompanying benchmark data, methodology description, error bars, workload definitions, or implementation results, rendering the primary result impossible to assess from the manuscript as presented.
minor comments (1)
  1. Abstract: the phrase 'representative ZKP benchmarks' is used without enumerating the specific workloads or providing a reference to a table or section that lists them.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address the single major comment below and are prepared to revise the abstract accordingly to improve immediate assessability of the results.

read point-by-point responses

  1. Referee: Abstract: the central performance claims (5–11× speedup and up to 3.8× area efficiency) are stated without any accompanying benchmark data, methodology description, error bars, workload definitions, or implementation results, rendering the primary result impossible to assess from the manuscript as presented.

    Authors: We acknowledge that the abstract, constrained by length, states the headline performance numbers without methodology, workload definitions, or supporting data. The full manuscript contains these details in Section 5 (Evaluation), which defines the representative ZKP workloads (including specific POLY- and EC-dominated phases from protocols such as Groth16 and Plonk), describes the FPGA/ASIC implementation and baselines, reports the measured speedups and area efficiencies, and includes error bars from repeated runs. To address the concern, we will revise the abstract to briefly reference the evaluation methodology and workload characteristics while preserving conciseness. revision: yes

Circularity Check

0 steps flagged

No significant circularity; design claims rest on empirical benchmarks

full rationale

This is an architecture paper proposing a new hardware-software co-design (TCore with Toom-Cook, flexible NoC, linked-list memory) and reporting measured speedups/area gains on ZKP benchmarks. No mathematical derivation chain, fitted parameters renamed as predictions, or self-citation load-bearing steps appear in the abstract or described content. The central claims are externally falsifiable via hardware implementation and workload measurements rather than reducing to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Review is based solely on the abstract; no explicit free parameters, axioms, or invented entities with independent evidence are detailed in the provided text. TCore is introduced as a new hardware component but lacks supporting details.

invented entities (1)
  • TCore no independent evidence
    purpose: Multi-precision modular multiplication core using Toom-Cook method with flexible NoC and linked-list memory
    New hardware component proposed to address precision scalability and utilization challenges.

pith-pipeline@v0.9.1-grok · 5775 in / 1421 out tokens · 45214 ms · 2026-06-28T08:26:04.298822+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

31 extracted references · 13 canonical work pages

  1. [1]

    Eli Ben Sasson, Alessandro Chiesa, Christina Garman, Matthew Green, Ian Miers, Eran Tromer, and Madars Virza. 2014. Zerocash: Decentralized Anonymous Payments from Bitcoin. In2014 IEEE Symposium on Security and Privacy. 459–474. doi:10.1109/SP.2014.36

    work page doi:10.1109/sp.2014.36 2014

  2. [2]

    Daniel Bernstein and Tanja Lange. [n. d.]. Elliptic Curve Formula Database (EFD). https://www.hyperelliptic.org/EFD/. Accessed: 2025-11-17

    2025

  3. [3]

    Bernstein and Tanja Lange

    Daniel J. Bernstein and Tanja Lange. 2007. Faster Addition and Doubling on Elliptic Curves. InAdvances in Cryptology – ASIACRYPT 2007, Kaoru Kurosawa (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 29–50

    2007

  4. [4]

    2025.Consensys/gnark: v0.14.0

    Gautam Botrel, Thomas Piellard, Youssef El Housni, Ivo Kubjas, and Arya Tabaie. 2025.Consensys/gnark: v0.14.0. doi:10.5281/zenodo.5819104

    work page doi:10.5281/zenodo.5819104 2025

  5. [5]

    Sean Bowe. 2017. BLS12-381: New zk-SNARK Elliptic Curve Construction. Blog post,Electric Coin CompanyBlog. https://electriccoin.co/blog/new-snark-curve/ Accessed: 2025-11-06

    2017

  6. [6]

    Alhad Daftardar, Brandon Reagen, and Siddharth Garg. 2024. Szkp: A scalable accelerator architecture for zero-knowledge proofs. InProceedings of the 2024 International Conference on Parallel Architectures and Compilation Techniques. 271–283

    2024

  7. [7]

    Xianglong Deng, Shengyu Fan, Zhicheng Hu, Zhuoyu Tian, Zihao Yang, Jiangrui Yu, Dingyuan Cao, Dan Meng, Rui Hou, Meng Li, et al. 2024. Trinity: A General Purpose FHE Accelerator.arXiv preprint arXiv:2410.13405(2024)

    work page arXiv 2024

  8. [8]

    S Goldwasser, S Micali, and C Rackoff. 1985. The knowledge complexity of interac- tive proof-systems. InProceedings of the Seventeenth Annual ACM Symposium on Theory of Computing(Providence, Rhode Island, USA)(STOC ’85). Association for Computing Machinery, New York, NY, USA, 291–304. doi:10.1145/22145.22178

    work page doi:10.1145/22145.22178 1985

  9. [9]

    Jens Groth. 2016. On the Size of Pairing-Based Non-interactive Arguments. In Proceedings, Part II, of the 35th Annual International Conference on Advances in Cryptology — EUROCRYPT 2016 - Volume 9666. Springer-Verlag, Berlin, Heidelberg, 305–326

    2016

  10. [10]

    Zhen Gu and Shuguo Li. 2019. A Division-Free Toom–Cook Multiplication-Based Montgomery Modular Multiplication.IEEE Transactions on Circuits and Systems II: Express Briefs66, 8 (2019), 1401–1405. doi:10.1109/TCSII.2018.2886962

    work page doi:10.1109/tcsii.2018.2886962 2019

  11. [11]

    Youssef El Housni and Gautam Botrel. 2022. EdMSM: Multi-Scalar-Multiplication for SNARKs and Faster Montgomery multiplication. Cryptology ePrint Archive, Paper 2022/1400. https://eprint.iacr.org/2022/1400

    2022

  12. [12]

    iden3. 2025. circom: zkSnark circuit compiler. GitHub repository. https://github. com/iden3/circom Accessed: 2025-11-06

    2025

  13. [13]

    Dai Cheol Jung, Scott Davidson, Chun Zhao, Dustin Richmond, and Michael Bed- ford Taylor. 2020. Ruche Networks: Wire-Maximal, No-Fuss NoCs : Special Session Paper. In2020 14th IEEE/ACM International Symposium on Networks-on- Chip (NOCS). 1–8. doi:10.1109/NOCS50636.2020.9241586

    work page doi:10.1109/nocs50636.2020.9241586 2020

  14. [14]

    Anatolii Karatsuba. 1963. Multiplication of multidigit numbers on automata. In Soviet physics doklady, Vol. 7. 595–596

    1963

  15. [15]

    Jongmin Kim, Sangpyo Kim, Jaewan Choi, Jaiyoung Park, Donghwan Kim, and Jung Ho Ahn. 2023. SHARP: A short-word hierarchical accelerator for robust and practical fully homomorphic encryption. InProceedings of the 50th Annual International Symposium on Computer Architecture. 1–15

    2023

  16. [16]

    Yoongu Kim, Weikun Yang, and Onur Mutlu. 2016. Ramulator: A Fast and Extensible DRAM Simulator.IEEE Computer Architecture Letters15, 1 (2016), 45–49. doi:10.1109/LCA.2015.2414456

    work page doi:10.1109/lca.2015.2414456 2016

  17. [17]

    Changxu Liu, Hao Zhou, Patrick Dai, Li Shang, and Fan Yang. 2024. PriorMSM: An Efficient Acceleration Architecture for Multi-Scalar Multiplication.ACM Trans. Des. Autom. Electron. Syst.29, 5, Article 77 (Aug. 2024), 26 pages. doi:10. 1145/3678006

    2024

  18. [18]

    Weiliang Ma, Qian Xiong, Xuanhua Shi, Xiaosong Ma, Hai Jin, Haozhao Kuang, Mingyu Gao, Ye Zhang, Haichen Shen, and Weifang Hu. 2023. GZKP: A GPU Accelerated Zero-Knowledge Proof System. InProceedings of the 28th ACM International Conference on Architectural Support for Programming Lan- guages and Operating Systems, Volume 2(Vancouver, BC, Canada)(ASPLOS 2...

    work page doi:10.1145/3575693.3575711 2023

  19. [19]

    Nicholas Pippenger. 1976. On the evaluation of powers and related problems. In17th Annual Symposium on Foundations of Computer Science (sfcs 1976). IEEE Computer Society, 258–263

    1976

  20. [20]

    Prasetiyo, Adiwena Putra, Joo-Young Kim, et al. 2024. Morphling: A Throughput- Maximized TFHE-based Accelerator using Transform-domain Reuse. In2024 IEEE International Symposium on High-Performance Computer Architecture (HPCA). IEEE, 249–262

    2024

  21. [21]

    Adiwena Putra, Prasetiyo, Yi Chen, John Kim, and Joo-Young Kim. 2023. Strix: An end-to-end streaming architecture with two-level ciphertext batching for fully homomorphic encryption with programmable bootstrapping. InProceedings of the 56th Annual IEEE/ACM International Symposium on Microarchitecture. 1319–1331

    2023

  22. [22]

    Andy Ray, Benjamin Devlin, Fu Yong Quah, and Rahul Yesantharao. 2024. Hard- caml MSM: A High-Performance Split CPU-FPGA Multi-Scalar Multiplication Engine. InProceedings of the 2024 ACM/SIGDA International Symposium on Field Programmable Gate Arrays(Monterey, CA, USA)(FPGA ’24). Association for Computing Machinery, New York, NY, USA, 33–39. doi:10.1145/36...

    work page doi:10.1145/3626202.3637577 2024

  23. [23]

    Louis Tremblay Thibault, Tom Sarry, and Abdelhakim Senhaji Hafid. 2022. Blockchain Scaling Using Rollups: A Comprehensive Survey.IEEE Access10 (2022), 93039–93054. doi:10.1109/ACCESS.2022.3200051

    work page doi:10.1109/access.2022.3200051 2022

  24. [24]

    Andrei L Toom. 1963. The complexity of a scheme of functional elements realizing the multiplication of integers, published in Soviet Math (translations of Dokl. Adad. Nauk. SSSR), 4

    1963

  25. [25]

    Charles. F. Xavier. 2022. PipeMSM: Hardware Acceleration for Multi-Scalar Multiplication. Cryptology ePrint Archive, Paper 2022/999. https://eprint.iacr. org/2022/999

    2022

  26. [26]

    Zhengbang Yang, Lutan Zhao, Peinan Li, Han Liu, Kai Li, Boyan Zhao, Dan Meng, and Rui Hou. 2025. LegoZK: A Dynamically Reconfigurable Accelerator for Zero- Knowledge Proof. In2025 IEEE International Symposium on High Performance Computer Architecture (HPCA). IEEE, 113–126

    2025

  27. [27]

    Sungwoong Yune, Hyojeong Lee, Adiwena Putra, Hyunjun Cho, Cuong Duong Manh, Jaeho Jeon, and Joo-Young Kim. 2025. ABC-FHE : A Resource-Efficient Accelerator Enabling Bootstrappable Parameters for Client-Side Fully Homomor- phic Encryption. arXiv:2506.08461 [cs.AR] https://arxiv.org/abs/2506.08461

    work page arXiv 2025

  28. [28]

    Jiaheng Zhang, Zhiyong Fang, Yupeng Zhang, and Dawn Song. 2020. Zero Knowledge Proofs for Decision Tree Predictions and Accuracy. InProceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security (Virtual Event, USA)(CCS ’20). Association for Computing Machinery, New York, NY, USA, 2039–2053. doi:10.1145/3372297.3417278

    work page doi:10.1145/3372297.3417278 2020

  29. [29]

    Yupeng Zhang, Daniel Genkin, Jonathan Katz, Dimitrios Papadopoulos, and Charalampos Papamanthou. 2017. vSQL: Verifying Arbitrary SQL Queries over Dynamic Outsourced Databases. Cryptology ePrint Archive, Paper 2017/1145. doi:10.1109/SP.2017.43

    work page doi:10.1109/sp.2017.43 2017

  30. [30]

    Ye Zhang, Shuo Wang, Xian Zhang, Jiangbin Dong, Xingzhong Mao, Fan Long, Cong Wang, Dong Zhou, Mingyu Gao, and Guangyu Sun. 2021. Pipezk: Acceler- ating zero-knowledge proof with a pipelined architecture. In2021 ACM/IEEE 48th Annual International Symposium on Computer Architecture (ISCA). IEEE, 416–428

    2021

  31. [31]

    Hao Zhou, Changxu Liu, Lan Yang, Li Shang, and Fan Yang. 2024. ReZK: A Highly Reconfigurable Accelerator for Zero-Knowledge Proof.IEEE Transactions on Circuits and Systems I: Regular Papers(2024)

    2024