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  <div id="root"><u-page id="lt-layout" class="c-lesPJm c-bXbWpx c-bAIfYK c-bAIfYK-ifdvvAQ-css"><nav class="c-lesPJm c-bXbWpx c-YtoYJ c-YtoYJ-ihTZtmw-css navbar"><u-row class="c-lesPJm c-bXbWpx c-ceAMyA c-ceAMyA-ibIRREI-css navbar-container"><a href="/"><img src="/assets/logo-with-text-fe10e011.svg" class="c-lesPJm c-lesPJm-ibJREvH-css"></a><u-box calssname="pc-system-menu" class="c-lesPJm c-bXbWpx c-bXbWpx-iejXDaP-css"><div class="pcNav"><div class="nav"><div class="item"><a href="https://zkbridge.com" target="_blank" rel="noreferrer" data-path="https://zkbridge.com" class="" style="white-space: nowrap;">zkBridge</a></div><div class="item"><a href="https://www.proof.cloud" target="_blank" rel="noreferrer" data-path="https://www.proof.cloud" class="" style="white-space: nowrap;">Proof Cloud<span class="c-lesPJm c-vTNff c-vTNff-iSlJrx-css">New</span></a></div><div class="item"><a class="" data-path="/research" style="white-space: nowrap;" href="/research">Research</a></div><div class="item"><a href="https://polyhedra.foundation/" target="_blank" rel="noreferrer" data-path="https://polyhedra.foundation/" class="" style="white-space: nowrap;">ZK🔥</a></div><div class="item"><span><div>Products</div><span class="iconWrap"><svg class="icon"><use xlink:href="#down"></use></svg></span></span></div><div class="item"><span><div>Developers</div><span class="iconWrap"><svg class="icon"><use xlink:href="#down"></use></svg></span></span></div><div class="item"><a class="" data-path="/ecosystem" style="white-space: nowrap;" href="/ecosystem">Ecosystem</a></div><div class="item"><a class="" data-path="/blog" style="white-space: nowrap;" href="/blog">Blog</a></div></div></div></u-box><a href="https://docs.google.com/forms/d/e/1FAIpQLSfPqAHspUYodFdVHOO19xd_YULerb_oFvdy3hSpNBVXFI7mNw/viewform" class="btn" target="_blank" rel="noreferrer" style="margin-left: auto; white-space: nowrap;">Get in Touch</a></u-row></nav><main class="c-lesPJm c-bXbWpx c-bAIfYK c-bAIfYK-iiGMPSL-css"><u-stack class="c-lesPJm c-bXbWpx c-cmpvrW c-cmpvrW-ieYwNdp-css"><u-box class="c-lesPJm c-bXbWpx c-bXbWpx-ibhNRjs-css header-bg"><video style="width: 100%; height: 100%; object-fit: cover; mix-blend-mode: lighten;" autoplay="" loop="" playsinline="" id="h-video" src="/assets/video-pc-homepage-ec4ab928.mp4"></video></u-box><u-col class="c-lesPJm c-bXbWpx c-kZgEvj c-kZgEvj-iicWWFN-css"><p class="c-lesPJm c-vTNff c-vTNff-ijVKKrX-css">Empowering interoperability and computation via ZK</p><u-space class="c-lesPJm c-gprnEz"></u-space><p class="c-lesPJm c-vTNff c-vTNff-ikCklre-css">Bringing interoperability and scalability to Web3 with <br>cutting-edge zero-knowledge proof systems</p><u-space class="c-lesPJm c-dFintv"></u-space><u-row class="c-lesPJm c-bXbWpx c-kWLZxY c-kWLZxY-iPJLV-css"><a target="_blank" href="https://www.proof.cloud" class="c-lesPJm c-lesPJm-dtVMWK-shape-round c-fzwWap c-btkMZW c-btkMZW-icAReUO-css"><p class="c-lesPJm c-vTNff c-vTNff-igQzQdu-css">Proof Cloud</p></a><a href="https://zkbridge.com" target="_blank" rel="noreferrer"><p class="c-lesPJm c-vTNff c-vTNff-ifouwww-css">zkBridge</p></a></u-row></u-col></u-stack><u-col class="c-lesPJm c-bXbWpx c-lfGTlH c-lfGTlH-iiVnBof-css"><div class="section-protocol"><div class="title">Introducing zkBridge Protocol</div><div class="desc"><div class="desc-img"></div><div class="desc-info"><p>zkBridge uses zkSNARKs to enable a prover to efficiently convince the receiver chain that a certain state transition happened on the sender chain. zkBridge consists of a block header relay network and an updater contract.</p><p>The block header relay network retrieves the block headers from the sender chain, generates proofs of the validity of the block headers, and sends the headers along with the proofs to the updater contract (set up on the receiver chain).</p><p style="margin-bottom: 50px;">The updater contract maintains a light-client state. It automatically adds block headers of the sender chain once the associated proofs are verified, and updates the current main chain of the sender chain.</p><div class="link" style="flex-direction: row;"><div class="btn" style="margin-right: 49px;">zkBridge Tech Paper<img src="/assets/arrow-link-5bed56e3.svg" class="c-lesPJm c-lesPJm-ihvoeZu-css"></div><br><div class="btn">Use zkBridge<img src="/assets/arrow-link-5bed56e3.svg" class="c-lesPJm c-lesPJm-ihvoeZu-css"></div></div></div></div></div><u-space class="c-lesPJm c-bKIGmr"></u-space><u-col class="c-lesPJm c-bXbWpx c-lfGTlH c-lfGTlH-idYtVoQ-css home-research"><p class="c-PJLV c-PJLV-ikuQAQy-css">Polyhedra Research</p><u-space class="c-lesPJm c-iCTRhL"></u-space><div class="swiper swiper-initialized swiper-horizontal"><div class="swiper-wrapper"><div class="swiper-slide swiper-slide-active" style="width: 380.667px; margin-right: 29px;"><div><a href="https://eprint.iacr.org/2019/1482.pdf" target="_blank" class="c-kEWnJJ"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-iipZLjU-css"><img src="/assets/Virgo@2x-d6005025.png" class="c-lesPJm c-lesPJm-igXzGi-css"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-ikppSAn-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ifvayZa-css">Virgo</p><p class="c-PJLV c-PJLV-jXJXCN-size-desc c-PJLV-idCKGWd-css ellipse-4">Virgo presents a powerful zero-knowledge argument scheme for layered arithmetic circuits without trusted setup based on Libra. It enjoys a fast prover as well as competitive proof size and fast verification time. Experiments show that it only takes 53 seconds to generate a proof for a circuit computing a Merkle tree with 256 leaves, at least an order of magnitude faster than all other succinct zero-knowledge argument schemes.</p><div class="mask" style="position: absolute; width: calc(100% - 40px); left: 20px; height: 19px; bottom: 40px; background: linear-gradient(rgba(14, 14, 14, 0) 0%, rgb(14, 14, 14) 100%);"></div><img src="/assets/link-d1cbb974.svg" class="c-lesPJm c-lesPJm-ihaCffO-css"></u-col></u-col></a></div></div><div class="swiper-slide swiper-slide-next" style="width: 380.667px; margin-right: 29px;"><div><a href="https://eprint.iacr.org/2020/1247.pdf" target="_blank" class="c-kEWnJJ"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-iipZLjU-css"><img src="/assets/Virgo __@2x-444e8990.png" class="c-lesPJm c-lesPJm-igXzGi-css"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-ikppSAn-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ifvayZa-css">Virgo ++</p><p class="c-PJLV c-PJLV-jXJXCN-size-desc c-PJLV-idCKGWd-css ellipse-4">Virgo++ generalizes the interactive proof of GKR protocol for layered circuits to arbitrary circuits, while preserving the optimal prover complexity that is strictly linear to the size of the circuits. Not only does our new protocol achieve optimal prover complexity asymptotically, but it is also efficient in practice. Our experiments show that it only takes less than one second to generate the proof for a circuit with more than a million gates, which is 13 times faster than the original interactive proof protocol on the corresponding layered circuit.</p><div class="mask" style="position: absolute; width: calc(100% - 40px); left: 20px; height: 19px; bottom: 40px; background: linear-gradient(rgba(14, 14, 14, 0) 0%, rgb(14, 14, 14) 100%);"></div><img src="/assets/link-d1cbb974.svg" class="c-lesPJm c-lesPJm-ihaCffO-css"></u-col></u-col></a></div></div><div class="swiper-slide" style="width: 380.667px; margin-right: 29px;"><div><a href="https://eprint.iacr.org/2022/1010.pdf" target="_blank" class="c-kEWnJJ"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-iipZLjU-css"><img src="/assets/Orion@2x-2cfa7214.png" class="c-lesPJm c-lesPJm-igXzGi-css"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-ikppSAn-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ifvayZa-css">Orion</p><p class="c-PJLV c-PJLV-jXJXCN-size-desc c-PJLV-idCKGWd-css ellipse-4">Orion is the latest proof system that utilizes the most recent advancements in the area. The system significantly reduces the proof generation time with practical proof size and verification time. The system is best suited for off-chain applications and zkEVMs.</p><div class="mask" style="position: absolute; width: calc(100% - 40px); left: 20px; height: 19px; bottom: 40px; background: linear-gradient(rgba(14, 14, 14, 0) 0%, rgb(14, 14, 14) 100%);"></div><img src="/assets/link-d1cbb974.svg" class="c-lesPJm c-lesPJm-ihaCffO-css"></u-col></u-col></a></div></div><div class="swiper-slide" style="width: 380.667px; margin-right: 29px;"><div><a href="https://eprint.iacr.org/2019/317.pdf" target="_blank" class="c-kEWnJJ"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-iipZLjU-css"><img src="/assets/Libra@2x-647a9a19.png" class="c-lesPJm c-lesPJm-igXzGi-css"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-ikppSAn-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ifvayZa-css">Libra</p><p class="c-PJLV c-PJLV-jXJXCN-size-desc c-PJLV-idCKGWd-css ellipse-4">Libra is a high performance proof system that achieves high speed by directly making an algorithm breakthrough without doing any trade-off. The system has been implemented, modified and optimized in our company’s core codebase. Our experiments show that the new implementation beats other proof systems by an order of magnitude.</p><div class="mask" style="position: absolute; width: calc(100% - 40px); left: 20px; height: 19px; bottom: 40px; background: linear-gradient(rgba(14, 14, 14, 0) 0%, rgb(14, 14, 14) 100%);"></div><img src="/assets/link-d1cbb974.svg" class="c-lesPJm c-lesPJm-ihaCffO-css"></u-col></u-col></a></div></div><div class="swiper-slide" style="width: 380.667px; margin-right: 29px;"><div><a href="https://eprint.iacr.org/2022/420.pdf" target="_blank" class="c-kEWnJJ"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-iipZLjU-css"><img src="/assets/Gemini@2x-55ca31c5.png" class="c-lesPJm c-lesPJm-igXzGi-css"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-ikppSAn-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ifvayZa-css">Gemini</p><p class="c-PJLV c-PJLV-jXJXCN-size-desc c-PJLV-idCKGWd-css ellipse-4">Gemini, a hardware-friendly zero-knowledge proof system, will help Polyhedra accelerate proof generation by leveraging specialized hardware.
The Gemini prover has multiple configurations with different time and memory tradeoffs, which can be selected depending on the execution environment and the proved statement. The output proof is independent of the chosen configuration. In a space-efficient configuration, the Gemini prover uses a logarithmic amount of memory, enabling super-fast hardware with limited memory.</p><div class="mask" style="position: absolute; width: calc(100% - 40px); left: 20px; height: 19px; bottom: 40px; background: linear-gradient(rgba(14, 14, 14, 0) 0%, rgb(14, 14, 14) 100%);"></div><img src="/assets/link-d1cbb974.svg" class="c-lesPJm c-lesPJm-ihaCffO-css"></u-col></u-col></a></div></div><div class="swiper-slide" style="width: 380.667px; margin-right: 29px;"><div><a href="https://eprint.iacr.org/2019/1047.pdf" target="_blank" class="c-kEWnJJ"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-iipZLjU-css"><img src="/assets/Marlin@2x-4b598fd1.png" class="c-lesPJm c-lesPJm-igXzGi-css"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-ikppSAn-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ifvayZa-css">Marlin</p><p class="c-PJLV c-PJLV-jXJXCN-size-desc c-PJLV-idCKGWd-css ellipse-4">Marlin, a zero-knowledge proof system with constant verifications, will help Polyhedra reduce the proof size and on-chain verification costs.
Marlin exploits a novel use of holography, where fast verification is achieved provided the statement being checked is given in encoded form. The result arguments have constant size and can be verified within several milliseconds.</p><div class="mask" style="position: absolute; width: calc(100% - 40px); left: 20px; height: 19px; bottom: 40px; background: linear-gradient(rgba(14, 14, 14, 0) 0%, rgb(14, 14, 14) 100%);"></div><img src="/assets/link-d1cbb974.svg" class="c-lesPJm c-lesPJm-ihaCffO-css"></u-col></u-col></a></div></div><div class="swiper-slide" style="width: 380.667px; margin-right: 29px;"><div><a href="https://eprint.iacr.org/2023/1271.pdf" target="_blank" class="c-kEWnJJ"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-iipZLjU-css"><img src="/assets/Pianist@2x-7e8f09f6.png" class="c-lesPJm c-lesPJm-igXzGi-css"><u-col class="c-lesPJm c-bXbWpx c-jWfHix c-jWfHix-ikppSAn-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ifvayZa-css">Pianist</p><p class="c-PJLV c-PJLV-jXJXCN-size-desc c-PJLV-idCKGWd-css ellipse-4">Pianist utilizes the power of distributed computing, it can combine hundreds of machines’ computation power into a unified proof generation machine. It offers unlimited horizontal scalability and perfect parallelism. We combined the technology in this system with Libra to get the best of both worlds.</p><div class="mask" style="position: absolute; width: calc(100% - 40px); left: 20px; height: 19px; bottom: 40px; background: linear-gradient(rgba(14, 14, 14, 0) 0%, rgb(14, 14, 14) 100%);"></div><img src="/assets/link-d1cbb974.svg" class="c-lesPJm c-lesPJm-ihaCffO-css"></u-col></u-col></a></div></div></div></div><u-row class="c-lesPJm c-bXbWpx c-etCyWe c-etCyWe-iPJLV-css"><img src="/assets/navButton-e4cddf5b.svg" class="c-lesPJm c-lesPJm-igpYNaN-css nav-btn-prev" style="left: -72px; position: absolute; top: 50%; translate: 0% -50%; z-index: 99;"><img src="/assets/navButton-e4cddf5b.svg" class="c-lesPJm c-lesPJm-ikbewLs-css nav-btn-next" style="right: -72px; position: absolute; top: 50%; translate: 0% -50%; z-index: 99;"></u-row></u-col><u-space class="c-lesPJm c-bKIGmr"></u-space><div class="Web3Stack"><p class="c-lesPJm c-vTNff c-vTNff-igtuUvj-css">Empower Web3 with ZK</p><u-space class="c-lesPJm c-kDiMpv"></u-space><u-switcher class="c-lesPJm c-bXbWpx c-dZdpDp c-dZdpDp-ibMAHaB-css"><u-nav class="c-lesPJm c-bXbWpx c-gUxpSV c-gUxpSV-iPJLV-css"><u-col data-active="true" class="c-lesPJm c-bXbWpx c-lhRXEC c-lhRXEC-iexRpyO-css"><p class="c-lesPJm c-vTNff c-vTNff-ikrxNDT-css">Interoperability</p><p class="c-lesPJm c-vTNff c-vTNff-iiSKDDb-css">Polyhedra Network implements infrastructures for Web3 interoperability across heterogeneous systems which guarantee strong security without extra trust assumptions.</p><u-space class="c-lesPJm c-cWMXGr"></u-space></u-col><u-col data-active="false" class="c-lesPJm c-bXbWpx c-lhRXEC c-lhRXEC-igBvfNL-css"><p class="c-lesPJm c-vTNff c-vTNff-ikrxNDT-css">Scalability</p><p class="c-lesPJm c-vTNff c-vTNff-iiSKDDb-css">Polyhedra Network designs and develops scalable and efficient zero-knowledge proof protocols for large-scale ZKP systems with distributed computing networks.</p><u-space class="c-lesPJm c-cWMXGr"></u-space></u-col><u-col data-active="false" class="c-lesPJm c-bXbWpx c-lhRXEC c-lhRXEC-igBvfNL-css"><p class="c-lesPJm c-vTNff c-vTNff-ikrxNDT-css">Modularity</p><p class="c-lesPJm c-vTNff c-vTNff-iiSKDDb-css">By applying a modular design, our infrastructures can become building blocks of other systems, and the developers can use our ZK technology without barriers.</p><u-space class="c-lesPJm c-cWMXGr"></u-space></u-col></u-nav><u-ul class="c-lesPJm c-bXbWpx c-gUxpSV c-gUxpSV-ihxukYx-css"><u-box data-active="true" class="c-lesPJm c-bXbWpx c-bXbWpx-ifHtNJQ-css"></u-box><u-box data-active="false" class="c-lesPJm c-bXbWpx c-bXbWpx-ieRHjxh-css"></u-box><u-box data-active="false" class="c-lesPJm c-bXbWpx c-bXbWpx-idqkyGi-css"></u-box></u-ul></u-switcher></div><u-space class="c-lesPJm c-bKIGmr"></u-space><div class="section-ecosystem"><div class="title"><p class="c-lesPJm c-vTNff c-vTNff-idwFlAN-css">Ecosystem</p><a href="/ecosystem">View More</a></div><div class="wrap"><div class="my-carousel"><div class="box 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class="item"><div>20M+</div><span>Total Messages</span></div><div class="item"><div>25+</div><span>Supported Blockchains</span></div><div class="item"><div>80+</div><span>Ecosystem Partners</span></div></div><u-space class="c-lesPJm c-bKIGmr"></u-space><u-col class="c-lesPJm c-bXbWpx c-lfGTlH c-lfGTlH-iPJLV-css c-jCuPJz"><p class="c-PJLV c-PJLV-iCfLFg-size-title c-PJLV-iMPOKo-css">The latest on 
Polyhedra Network</p><u-space class="c-lesPJm c-iCTRhL"></u-space><u-ul class="c-lesPJm c-bXbWpx c-gUxpSV c-gUxpSV-iPJLV-css"><a href="https://blog.polyhedra.network/introducing-the-bitcoin-messaging-protocol-with-zkbridge" target="_blank" class="c-kEWnJJ c-kEWnJJ-ieSikyR-css"><u-col class="c-lesPJm c-bXbWpx c-ciWKcL c-ciWKcL-igBkLoP-css"><u-row class="c-lesPJm c-bXbWpx c-ceAMyA c-ceAMyA-ikSpslS-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ihsYHIj-css">Introducing the Bitcoin Messaging Protocol with zkBridge</p><u-box class="c-lesPJm c-bXbWpx c-bXbWpx-icLkPZK-css arrow"></u-box></u-row><div class="c-hOoOgu">News</div></u-col></a><a href="https://blog.polyhedra.network/ethereum-single-slot-finality" target="_blank" class="c-kEWnJJ c-kEWnJJ-ieSikyR-css"><u-col class="c-lesPJm c-bXbWpx c-ciWKcL c-ciWKcL-igBkLoP-css"><u-row class="c-lesPJm c-bXbWpx c-ceAMyA c-ceAMyA-ikSpslS-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ihsYHIj-css">Ethereum Single Slot Finality</p><u-box class="c-lesPJm c-bXbWpx c-bXbWpx-icLkPZK-css arrow"></u-box></u-row><div class="c-hOoOgu">News</div></u-col></a><a href="https://blog.polyhedra.network/secure-and-efficient-interoperability-on-arbitrum-with-zkbridge" target="_blank" class="c-kEWnJJ c-kEWnJJ-ieSikyR-css"><u-col class="c-lesPJm c-bXbWpx c-ciWKcL c-ciWKcL-igBkLoP-css"><u-row class="c-lesPJm c-bXbWpx c-ceAMyA c-ceAMyA-ikSpslS-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ihsYHIj-css">Secure and Efficient Interoperability on Arbitrum with zkBridge</p><u-box class="c-lesPJm c-bXbWpx c-bXbWpx-icLkPZK-css arrow"></u-box></u-row><div class="c-hOoOgu">News</div></u-col></a><a href="https://polygon.technology/blog/polyhedra-network-is-building-a-zk-powered-cross-chain-bridge-on-polygon" target="_blank" class="c-kEWnJJ c-kEWnJJ-ieSikyR-css"><u-col class="c-lesPJm c-bXbWpx c-ciWKcL c-ciWKcL-igBkLoP-css"><u-row class="c-lesPJm c-bXbWpx c-ceAMyA c-ceAMyA-ikSpslS-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ihsYHIj-css">Polyhedra Network is Building a ZK-Powered Cross-Chain Bridge on Polygon</p><u-box class="c-lesPJm c-bXbWpx c-bXbWpx-icLkPZK-css arrow"></u-box></u-row><div class="c-hOoOgu">News</div></u-col></a><a href="https://blog.polyhedra.network/proving-full-node-of-ethereum-in-zk" target="_blank" class="c-kEWnJJ c-kEWnJJ-ieSikyR-css"><u-col class="c-lesPJm c-bXbWpx c-ciWKcL c-ciWKcL-igBkLoP-css"><u-row class="c-lesPJm c-bXbWpx c-ceAMyA c-ceAMyA-ikSpslS-css"><p class="c-PJLV c-PJLV-eUBfuB-size-subTitle c-PJLV-ihsYHIj-css">Proving full node of Ethereum in ZK</p><u-box class="c-lesPJm c-bXbWpx c-bXbWpx-icLkPZK-css arrow"></u-box></u-row><div class="c-hOoOgu">News</div></u-col></a></u-ul></u-col><u-space class="c-lesPJm c-dZEklL"></u-space><u-col class="c-lesPJm c-bXbWpx c-lfGTlH c-lfGTlH-ijOXLTs-css"><p class="c-lesPJm c-vTNff c-vTNff-idwFlAN-css">Backers</p><u-space class="c-lesPJm c-hGsNCb"></u-space><u-grid class="c-bKdkJy c-bKdkJy-ihhMvDi-css"><a class="partnerItem" href="https://labs.binance.com/" target="_blank" rel="noreferrer" style="width: 282px; 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