# Hardware for ZKP

By [bluepoint](https://paragraph.com/@bluepoint) · 2022-04-16

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It’s a summary of article from [Georgios Konstantopoulos](https://www.paradigm.xyz/team/gakonst) and my understanding.

[https://www.paradigm.xyz/2022/04/zk-hardware](https://www.paradigm.xyz/2022/04/zk-hardware)

Introduction
============

ZKPs are slow and expensive to produce due to a large number of expensive math operations.

ZKP usage
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*   Outsourced Verifiable Computation
    

**ZKPs allow a third party provider to also output a proof of computational integrity which guarantees the output you received is correct.**

*   Private Computation
    

**ZKPs allow you to selectively hide some or all inputs around a computational statement.**

![](https://storage.googleapis.com/papyrus_images/f1665b239023221aad128e749a1ef2d131389452ee8c9ba16fa7b8c61070aa00.jpg)

Optimization is necessary
=========================

ZKP is generated like below:

1.  Computation Expression
    
2.  Generate proof
    

The computation in proof generation mostly reside in:

1.  MSMs: **Multiplications** over large vectors of numbers (field or group elements), specifically [variable-base and fixed-base multi-scalar multiplications](https://youtu.be/Bl5mQA7UL2I)
    
    *   Typically 70% time
        
    *   Vector of 2e25 elements
        
    *   Can be parallel but still slow with hundereds of cores
        
2.  FFTs: **Fast Fourier Transforms** (FFTs) and Inverse FFTs
    
    *   Typically 30% time
        
    *   Data shuffling
        
    *   Not suitable for computing cluster and need much bandwidth
        

Hardware Solution
=================

![](https://storage.googleapis.com/papyrus_images/3eda57bc86ebf77e3e55f22ae35cb1266854a58eaf6c187d3b66649bc2d2abb2.jpg)

Conclusions
===========

Mining Market:

*   Bitcoin: $15B
    
*   Ethereum: $17B
    
*   **ZKP: may be similar size to Bitcoin/Ethereum**
    

My understanding
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1.  GPU is the best option from the developer’s perspective, as programming friendliness is very important in industry’s early stage and there are more than 2 million GPU developers worldwide.
    
2.  In the case when cost & power is more important, FPGA is the best option.
    
3.  Once the ZKP mining industry really emerges, ASIC will prevail, just like bitmain’s product.
    

Reference
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[https://people.iiis.tsinghua.edu.cn/~gaomy/pubs/pipezk.isca21.pdf](https://people.iiis.tsinghua.edu.cn/~gaomy/pubs/pipezk.isca21.pdf)

[https://hackmd.io/@yezhang/S1\_KMMbGt#zkEVM](https://hackmd.io/@yezhang/S1_KMMbGt#zkEVM)

[https://www.usenix.org/conference/usenixsecurity18/presentation/wu](https://www.usenix.org/conference/usenixsecurity18/presentation/wu)

[https://github.com/ZcashFoundation/zcash-fpga](https://github.com/ZcashFoundation/zcash-fpga)

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*Originally published on [bluepoint](https://paragraph.com/@bluepoint/hardware-for-zkp)*