GPU Revolution: How We Use zk-SNARKs to Make Ethereum 1000 Times Faster

This article will analyze a key technological breakthrough: by combining high-performance GPUs with zk-SNARKs, we are increasing the operational efficiency of Ethereum by hundreds or even thousands of times. This not only addresses the long-standing performance bottlenecks of blockchain but also provides a viable technological path for the future of Web3 infrastructure.

If you have ever wondered: why is Ethereum running slowly and why are transaction costs so high? Or are you focusing on the key driving factors of the next generation of blockchain technology? Then this article will provide you with clear answers.

The Essence of the Problem: Why is Blockchain Like a Congested Highway?

Think of Ethereum as a highway. Today, all users and applications are competing for limited lane resources, resulting in network congestion, slow transaction processing, and high gas fees.

There are only two traditional solutions:

• Build more lanes - that is to construct Layer 2 networks (such as Rollups)
• Make vehicles smaller — that is, compress transaction data.

But what if there was a way to “teleport” vehicles instead of continuing to squeeze in the lanes? This is precisely the paradigm shift brought by zk-SNARKs. The core idea is: without the need to transmit all the transaction data itself, we can validate the authenticity of the transaction simply by generating a mathematical proof. In other words, we no longer need every vehicle to travel on the highway; instead, we can directly verify that “these vehicles have indeed reached the destination.” This not only reduces the burden of data transmission but also allows for the compatibility of “high throughput + strong security + trustless verification.”

The Verge: The Next Evolution of Ethereum

Ethereum is currently advancing a grand technical blueprint - The Verge, which you can understand as Ethereum’s “Slimming Plan.” The goal is to significantly lower the threshold for running Ethereum nodes, making it as simple as running an App on a mobile phone. In the future, everyone will be able to easily join the Ethereum network without relying on a high-performance gaming computer.

But there is a key technical challenge behind this plan: it requires completing millions of complex mathematical operations in a very short time.

This is exactly the breakthrough direction that the Polyhedra team is focused on - how to use GPU to accelerate large-scale ZK computations, significantly improving execution efficiency while ensuring verification security.

Technical Challenges: This set of data will overturn your understanding

To understand the complexity we are dealing with, here is the real scale of current on-chain operations on Ethereum:

• Consensus Verification： Each block contains approximately 90 million SHA 2-256 hash calculations and 2,048 BLS digital signature verifications.
• State Transition Proofs： Each Block requires approximately 500,000 Keccak hash operations.
• Current bottleneck:
  The CPU-based zero-knowledge proof system (Prover) can currently process only about 2 million Poseidon hash computations per second.

The real challenge lies in the fact that we need to use zk-SNARKs technology to complete all the calculations mentioned above, which undoubtedly greatly increases the computational complexity.

Breakthrough: The Power Revolution of GPUs

As we all know, GPUs are favorites among gamers and AI engineers. However, in reality, these graphics processing units demonstrate capabilities far superior to CPUs when handling the large-scale parallel mathematical computations required for zk-SNARKs.

At Polyhedra, we have optimized the ZK proof system natively for GPU and achieved groundbreaking performance metrics:

Performance leap, far beyond expectations.

• Basic mathematical operations (Mersenne 31 field) accelerated by 362 times
• Complex cryptographic operations (BN 254 elliptic curve) accelerated by up to 2826 times
• A zero-knowledge computation that originally took 21 minutes has now been compressed to only 450 milliseconds.

In other words, this is equivalent to your daily commute time during rush hour dropping from 20 minutes to less than half a second. This is not incremental optimization, but a paradigm-level leap in computation.

Why is this breakthrough relevant to you?

1. Lower transaction costs: Faster proof generation means a significant reduction in overall computational costs, leading to lower Gas fees. A win-win for users and the network.
2. Stronger security guarantees: Do you remember we mentioned that Ethereum has an annual security budget of over 40 million USD? With our technology, light nodes can easily verify the entire Ethereum consensus chain, enjoying mainnet-level security guarantees without the need for large resource expenditures.
3. More popular nodes can run, mobile phones can run Ethereum: Our continuous optimization of performance and efficiency is making it possible to run Ethereum nodes on ordinary devices. In the future, verifying blockchain data may only require a mobile phone.

Technical Core: How We Achieved It

1. GPU Native Design: CUDA Optimized Sumcheck Protocol

Our Sumcheck implementation built on CUDA fully leverages the parallel computing advantages of GPUs:

• Design customized CUDA kernels for field operations (addition, multiplication, exponentiation)
• Maximize GPU bandwidth utilization using merged memory access patterns (RTX 4090 measured bandwidth up to 1008 GB/s)
• Use warp-level primitives to achieve efficient reduction operations.

This level of deep customization allows the Sumcheck protocol to no longer be constrained by the serial bottleneck of the CPU.

2. Memory is King: Bandwidth Bottleneck Optimization Traditional views suggest that the ZK Prover’s computational bottleneck lies in computing power, but our empirical evidence shows that - Sumcheck is a typical memory bandwidth bottleneck issue:

• Memory throughput analysis: Bandwidth utilization reaches theoretical maximum of 95% +
• Data structure optimization: Using Structure-of-Arrays (SoA) instead of traditional Array-of-Structures (AoS) structures
• SM unit utilization improvement: Achieving optimal hardware occupancy through optimizing thread block configuration.

By solving the memory throughput problem, we have turned ZK computation into a truly efficient streaming task.

3. Customized optimization strategies for different numerical domains

Different cryptographic fields have different operational characteristics, and we have tailored optimization paths for each mainstream field:

• Mersenne 31 (M 31): 31-bit integer optimization, efficient modular arithmetic structure
• M 31 ext 3: Extended field support, accommodating polynomial expansion and low overhead.
• BN 254: Custom multiplier based on the Montgomery algorithm, designed for 254-bit large integer fields.

This highly targeted underlying optimization makes our ZK Prover both versatile and extremely efficient.

Performance Data Breakdown: Where Optimization Occurs

We have not only made it “much faster,” but also pushed ZK performance to unprecedented heights. Here are the actual performance data:

Technical Architecture Revealed: The Truth Under the Hood

GKR Protocol Stack: Accelerated Core

Our acceleration optimization focuses on the GKR (Goldwasser-Kalai-Rothblum) protocol, specifically including:

• Linear GKR layer: used for handling addition and multiplication gates
• Sumcheck Protocol: The performance bottleneck, accounting for nearly 50% of total CPU computation time.
• Polynomial Evaluation Phase: Reducing computation time on the GPU from 8.4 seconds to 9.5 milliseconds

Detailed Explanation of GPU Kernel Design

Phase One: Polynomial Evaluation

• Parallel computing on 2 ^n points
• Use shared memory cache coefficient to improve access speed
• Achieve efficient reduction operations with warp shuffle
• Phase Two: Challenge Generation
• Execute Fiat-Shamir hash operations internally on the GPU to avoid frequent switching between CPU and GPU.
• Reduce communication latency between CPU and GPU

Memory Transmission Optimization: Unblocking the “Last Mile” of Data Flow

We have also made systematic optimizations in CPU-GPU interaction to ensure that bandwidth does not become a bottleneck:

• PCIe data throughput optimization: Processing 2 ^{ 27 } elements takes only 737 milliseconds
• Pinned Memory: Supports “zero-copy” data transfer, reducing copy costs.
• Asynchronous operation scheduling: computation and communication are carried out in parallel, maximizing resource utilization.

To be honest: challenges still exist

We always adhere to transparency - GPU acceleration is not a万能解法, and in practice, we have also encountered many technical bottlenecks.

1. Memory bandwidth has reached its peak.

• Even though the H100 has a bandwidth of up to 3.35 TB/s, it can still become a performance bottleneck under heavy load.
• In comparison: larger elliptic curve fields (such as BN 254) reach the ceiling faster than smaller fields (such as M 31)

2. GPU memory capacity is limited

• RTX 4090 runs out of memory when processing 2 ^{ 29 } elements
• A refined memory scheduling strategy is needed during actual deployment to avoid overflow risks.

3. Trade-off between Domain Size and Performance

4. Comparison of “GPU Advantages”: When did it start to surpass CPU?

Cross-platform performance testing

We conducted benchmarking on different levels of GPUs, covering consumer-grade and data center-grade hardware:

Consumer-grade GPU

• RTX 3090: 936 GB/s memory bandwidth for up to 951x faster performance
• RTX 4090: Memory bandwidth 1008 GB/s, performance improvement up to 1565 times
• Data Center GPU
• NVIDIA H100: Bandwidth up to 3.35 TB/s, performance improvement of up to 2826 times.

The conclusion is clear: memory bandwidth is the key variable for accelerating zk-SNARKs.

Looking Ahead: Our Roadmap

We are far from stopping; we will continue to tackle the following goals:

• More extreme acceleration: For specific operations, the goal is to achieve a speed increase of 10,000 times.
• Broader hardware compatibility: full coverage from high-performance gaming graphics cards to data center-grade accelerator cards.
• Native Integration of Ethereum: We are collaborating with the Ethereum client development team to directly integrate our GPU ZK proof stack into the L1 layer.

Join this wave of transformation! ###

This is not just an enhancement in speed, but a complete redefinition of Blockchain accessibility. No matter who you are, you can find a way to participate:

• Developer: Welcome to check out our Expander and CUDA repositories to build the future together.
• Learners: Follow our research seminars and technical deep dives for continuous updates that stay relevant.
• Everyone: Spread this technology! The more people understand it, the closer the future of Web3 will be.

Core Viewpoints Review

We are at an exciting technological turning point. The combination of zk-SNARKs and GPU acceleration is not just a marginal improvement in performance, but a paradigm shift.

We are redefining the boundaries of speed, cost, and usability of Ethereum.

Overview of Key Technological Achievements:

• Production-ready ZK proof implementation with over 1000x acceleration
• GPU memory bandwidth utilization exceeds 95%
• Open source implementation, ready for integration at any time

The future of Web3 is not only decentralized but also incredibly accessible, and it is coming faster than you might imagine.

What aspect of these developments interests you the most? Feel free to leave a comment or interact with me on Twitter; we are very happy to delve into these technical details!

The future belongs to speed, and it belongs to you. See you next time, keep building, not just fast!