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Web 3 中的零知识证明

作译者：高承实

出版时间：2024-09 千字数：403 版次：01-01 页数：288

开本：16开装帧： I S B N ：9787121488115

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作者简介

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目 录
第1 章 Web 3 新基建崛起 ..................................................................................................... 001
1.1 Web 3 主流叙事 ···············································································.001
1.1.1 史前叙事 ···············································································.002
1.1.2 公链降临 ···············································································.004
1.1.3 去中心化金融DeFi 创世 ····························································.007
1.1.4 非同质化代币NFT 异军突起 ······················································.012
1.1.5 链游GameFi 先声夺人 ······························································.017
1.2 Web 3 基础设施体系初现 ···································································.020
1.2.1 Web 3 基础设施框架 ·································································.020
1.2.2 数据服务 ···············································································.023
1.2.3 去中心化身份堆栈 ···································································.030
1.2.4 安全与审计 ············································································.034
1.3 零知识证明叙事升温 ·········································································.038
1.3.1 零知识证明的奥妙 ···································································.039
1.3.2 自主掌控隐私 ·········································································.041
1.3.3 破解可扩展性难题 ···································································.045
第2 章 揭开零知识证明的神秘面纱 .................................................................................... 050
2.1 “证明”的历史 ···············································································.050
2.1.1 从归纳推理到演绎推理 ·····························································.050
2.1.2 形式化符号语言推理 ································································.051
2.1.3 计算机证明 ············································································.052
2.1.4 交互式证明 ············································································.053
2.2 绕不开的计算复杂性 ·········································································.054
2.2.1 基本概念 ···············································································.054
2.2.2 P 问题、NP 问题与NPC 问题 ·····················································.059
2.2.3 电路复杂性 ············································································.064
2.3 零知识证明的基本原理 ······································································.068
2.3.1 故事中的零知识证明 ································································.068
2.3.2 模拟器定义“零知识性” ··························································.071
2.3.3 提取器定义“可靠性” ·····························································.075
2.3.4 从交互式证明到简洁非交互式证明 ··············································.078
第3 章 零知识简洁非交互论证系统的构造 ........................................................................ 091
3.1 构造零知识简洁非交互论证系统的主要步骤 ···········································.092
3.1.1 SNARK 系统的底层 ·································································.092
3.1.2 可验证计算及其设计 ································································.095
3.2 将计算需求转化为电路 ······································································.103
3.2.1 将问题转化为程序 ···································································.103
3.2.2 将程序转化为计算电路 ·····························································.104
3.3 信息论模型的构造 ············································································.112
3.3.1 LIP 模型 ················································································.113
3.3.2 IOP 模型 ···············································································.114
3.4 证明多项式 ·····················································································.115
3.4.1 FRI 承诺 ················································································.115
3.4.2 KZG10 承诺 ···········································································.120
3.4.3 IPA 承诺 ················································································.123
3.4.4 不同方案的对比 ······································································.126
3.5 非交互及零知识的实现 ······································································.127
3.5.1 非交互性 ···············································································.127
3.5.2 零知识 ··················································································.130
3.6 小结······························································································.132
3.6.1 ZK-SNARK 的分类 ··································································.132
3.6.2 更多的组合和递归 ···································································.133
第4 章 零知识证明的主流实现方案 .................................................................................... 136
4.1 零知识证明技术和应用发展 ································································.137
4.1.1 零知识证明的技术发展 ·····························································.137
4.1.2 重新定义区块链运作方式 ··························································.138
4.2 ZK-SNARK ····················································································.141
4.2.1 工作原理 ···············································································.142
4.2.2 主要协议 ···············································································.142
4.3 ZK-STARK ·····················································································.152
4.3.1 工作原理 ···············································································.152
4.3.2 ZK-SNARK 与ZK-STARK ·························································.159
4.4 Bulletproofs ·····················································································.163
4.4.1 工作原理 ···············································································.163
4.4.2 应用场景 ···············································································.169
4.5 ZKP 系统的比较维度 ········································································.171
4.5.1 效率和安全维度 ······································································.171
4.5.2 底层技术维度 ·········································································.173
第5 章 零知识证明“众神殿” ............................................................................................. 177
5.1 市场机会 ························································································.178
5.1.1 基础设施 ···············································································.178
5.1.2 身份与安全 ············································································.184
5.1.3 DeFi 与支付 ···········································································.187
5.1.4 硬件加速 ···············································································.191
5.1.5 NFT 交易 ···············································································.193
5.2 Web 3 系统扩容 ···············································································.194
5.2.1 zkSync ··················································································.195
5.2.2 StarkNet ················································································.201
5.2.3 Scroll ····················································································.206
5.2.4 Polygon zkEVM ·······································································.212
5.3 挑战可交互性 ··················································································.215
5.3.1 跨链桥概述 ············································································.215
5.3.2 ZKP 跨链原理及难点 ································································.219
5.3.3 实现以太坊PoS 轻客户端 ··························································.220
5.3.4 将IBC 引入以太坊 ···································································.223
5.3.5 分布式零知识证明 ···································································.227
5.4 数字身份解决方案 ············································································.229
5.4.1 去中心化身份堆栈 ···································································.229
5.4.2 ZK 勋章证明声誉 ····································································.232
5.4.3 ZKDID 预言机 ········································································.234
5.4.4 ZK-KYC 助力合规 ···································································.238
5.5 博弈中的隐私支付 ············································································.242
5.5.1 隐私币 ··················································································.243
5.5.2 隐私交易网络 ·········································································.248
5.5.3 隐私智能合约 ·········································································.251
第6 章 Web 3 之外的零知识证明 ........................................................................................ 254
6.1 零知识证明赋能生成式AI ··································································.255
6.1.1 为ML 上链提供基础设施 ··························································.256
6.1.2 实现信任证明 ·········································································.257
6.1.3 开拓游戏新属性 ······································································.257
6.2 抵抗虚假信息 ··················································································.259
6.2.1 音频的ZK 证明 ·······································································.259
6.2.2 新闻照片的ZK 证明 ·································································.260
6.3 分布式智能电网的安全控制 ································································.262
6.4 医疗数据保护与安全共享 ···································································.264
6.4.1 医疗数据安全共享 ···································································.264
6.4.2 医疗数据安全采集 ···································································.267
参考文献 ....................................................................................................................................... 271
后记 ............................................................................................................................................... 277

前 言
  零知识证明和Web 3 的未来
什么是零知识证明？
零知识证明的英文是Zero-Knowledge Proof，是指证明者能够在不向验证者提供任何有用信息的情况下，使验证者相信某个论断是正确的。从这个描述，我们就可以大体想象得出，零知识证明对我们的生活有多么重要！
1. 零知识证明带来了新的信任建立方式
信任是人类社会得以建立和发展最重要的基础之一，如果没有信任，人类社会将不复存在。那么如何建立信任呢？
从古至今，人类可能一共只有4 种信任建立的方式。
第一种是建立在熟人之间长期反复博弈基础上的信任。经过长期交往，我们可以得出一些结论，比如张三可信，李四不可信，王五在一些方面可信，但在另一些方面就不一定可信等。这种信任，一方面与某个人的能力大小有关，另一方面也是此人的一种相对的天然属性。这种信任是民间社会得以建立和发展的重要基础，民间交往、借贷等经济活动也都建立在这样的信任之上。
如果我们把这种信任做进一步扩展，由个人扩展到组织，就形成了评级机构信用评级的评价对象，这也是经济社会中信用贷开展的前提和基础。如果扩展到国家，这种信任就是一个国家的主权信用评级。在信用评级领域，这种信任更多的是评价对象是否有能力偿还贷款，而不一定与其本来的属性有关。
第二种是建立在中心化权威机构做信任背书基础上的信任。比如我们都会相信政府机构会秉公办事，我们也会相信中央银行发行的货币可以作为通货来使用。然而，有时我们也不得不相信某些机构和组织不会骗我们，但同时我们在内心深处又充满了对它们的不信任。
第三种是区块链带来的去中心化信任。区块链带来的去中心化信任不同于熟人建立在长期反复博弈基础上的信任，也不同于由中心化权威机构做信任背书建立起来的信任。在通过各种去中心化金融基础设施应用DeFi 实施交易时，我们并不知道和我们交易的人是谁，这个人是否可信就更无从谈起了，这种交易也没有一个权威可信的第三方为交易双方做信任背书，我们相信的是区块链的共识机制和DeFi 这种去中心化金融交易应用的强制执行力。
区块链带来的这种信任，在某种程度上与由中心化权威机构做信任背书形成的信任有相似之处。比如在上海证券交易所交易股票，我们同样不知道与我们交易的对方是谁，也不知道这个人是否可信，我们相信的是上海证券交易所建立的一整套保障机制。如果真的在交易过程中出现问题，我们相信上海证券交易所会帮我们处理。这种信任是建立在由一个中心化权威机构做信任背书的基础上的，而区块链带来的信任，一是建立在由所有人认同且由所有人努力保障的共识机制之上的信任，二是对各种去中心化智能合约的强制执行力的信任。这种信任不依赖任何一个中心化机构，是一种对去中心化体系的信任。
零知识证明则带来了第四种信任，即建立在数学基础上的信任。这种建立在数学基础上的信任，不看交易双方之前是否认识，更不关心对方是否可信，这种信任也不需要任何机构做信任背书，甚至不需要建立在任何强大的共识机制上。如果非要说有共识，那么这种共识就是数学证明。只要交易双方都相信数学，这种信任就可以得到证明，信
任关系就可以建立起来。
2. 去中心化应用带来了数字世界中新的业务组织方式
人类从古至今几乎所有生产生活的组织方式，都是介于中心化和去中心化之间的，是不同程度的中心化和去中心化的组合。人类社会也可以说从来不存在百分之百的中心化，也不存在百分之百的去中心化。但在信息技术出现后，建立在信息技术能力的不对称基础上，基于业务组织管理需要，在原本去中心化的网络通信协议基础上，建立了中心化的业务系统组织管理载体——万维网，即World Wide Web。建立在万维网基础上的各种业务系统，几乎都是中心化的系统。无论是以前的信息互联网、当前比较成熟的消费互联网，还是正在实施中的工业互联网和产业互联网，都是中心化的系统。
区块链则在数字世界中为去中心化的业务组织管理方式提供了基础设施。在区块链之上，近几年迅速出现了去中心化金融DeFi、非同质化代币NFT、链游GameFi，以及去中心化社交网络SocialFi 等种类繁杂、数量众多的去中心化应用。虽然这些建立在区块链上的去中心化应用目前主要聚焦在虚拟数字货币相关领域，大多是由投机力量和创新力量综合驱动的，应用规模和应用范围也还比较有限，但其发展前景不容小觑。区块链这种基础设施建立以后，这些去中心化应用一旦与现实世界结合并得到广泛应用，就将在极深的层次上改变当前人类社会的生产生活组织方式，在总体上带来效率的极大提升，并带来交易成本的极大下降。
3. Web 3 的概念界定及其发展困境
基于用户对数据可实施的操作，人们把互联网的发展划分为Web 1.0、Web 2.0 和Web3.0 这3 个阶段。Web 1.0 是指用户仅能读取数据，其典型代表就是20 世纪末的信息门户网站。信息门户网站把相关信息数字化后呈现给用户，用户仅能阅读，没有办法上传或写入数据。以BBS 为开端的互联网被称为Web 2.0，在这个阶段，用户不仅可以从网
络上读取数据，而且可以自行写入数据。
Web 1.0 和Web 2.0 阶段的互联网大多以平台为运营主体。虽然用户可以读或写数据，但用户并不拥有数据，即使数据是用户自己上传并写入的，数据的所有权归平台所有。平台利用这些数据赚取了超额利润，但这些超额利润却没有分配给贡献数据的用户。于是，在区块链去中心化的背景下，业界很多人提出了Web 3.0 的概念。Web 3.0 试图通
过区块链相关技术，帮助用户实现数据的可读、可写和可拥有。
在编者看来，Web 3.0 的愿景在技术上难以实现。一是数据的载体非常广泛，其边际复制成本又几乎为零，这让我们难以将数据局限在一个固定的范围内；二是数据的复制在某种程度上也是难以追踪的，这让确保数据可拥有变得难以实现。
此外，即使通过区块链，也同样难以实现数据可拥有。区块链全节点账本数据同步的技术特性，决定了区块链上难以承载大规模数据。Web 2.0 时代，平台利用数据赚取超额利润的数据就是大数据，而不是小数据或关键数据。这就使得传统的在Web 2.0 时代产生的数据所有权的问题，在区块链或Web 3.0 的环境中也同样难以解决。
当然，数据可读、可写、可拥有，确实在区块链或Web 3.0 的环境下有实现特例。这种特例就是我们平常所说的各种虚拟数字货币，如“同质化代币”FT、“非同质化代币”NFT，还有未来的分布式身份得以建立的“灵魂绑定通证”SBT，以及介于各种同质化代币FT 和非同质代币NFT 之间的“半匀质化代币”SFT。这类内容尽管是数据，但又不是我们通常意义上的数据，更不是我们目前所讲的作为生产要素的数据。
同质化代币FT、非同质化代币NFT、灵魂绑定通证SBT、半匀质化代币SFT 等之所以能在区块链及Web 3.0 基础上实现可读、可写、可拥有，是因为我们对其认定和使用做了极其严格的界定。同质化代币FT、非同质化代币NFT、半匀质化代币SFT 被我们定位为数字资产，灵魂绑定通证SBT 被我们定位为身份证明，而这些内容只有在共识
机制作用下，才会在其所关联的链上或应用中被认定为有效，一旦跨出了特定区域和环境，承载这些内容的数据就是“垃圾”。这也是区块链领域经常讲的主权区域。
抛开前文提到的人们对Web 3.0 的各种预期和设想，从现实的技术实现和可能性角度，编者将Web 3 定义为建立在区块链基础上的各种去中心化基础设施和去中心化应用。在这个定义之下，Web 3 就包括了Web 3.0。Web 3.0 则被定义为建立在单条区块链之上的去中心化基础设施和去中心化应用。Web 3.0 的典型代表就是建立在以太坊之上的以
太坊生态，该生态是将以太坊区块链作为基础，加上以太坊之上的二层网络甚至三层网络扩展，以及构建在以太坊、以太坊的二层网络及三层网络之上的各种去中心化应用的集合。
无论是现在，还是未来，以太坊虽然有可能一家独大，但世界上绝不可能只有一条以太坊区块链。于是，就有了链与链之间的跨链需求和跨链应用。Web 3 的下一步发展则是基于去中心化实现链与链之间的连通。目前的跨链大多还是一个连接不同区块链网络的单独应用，这些应用所实现的功能也几乎都是对源链共识结果在目标链上的扩展。说得直白一些，目前的跨链基本上都是用一套机制认可了源链上的一个共识结果，并将其锁定后在目标链上再生成一个对应的结果。该结果在跨链机制和目标链的共同认可下，成为目标链上的一个新的共识结果。这种跨链无论从安全性，还是功能上都还非常简陋。
未来，除了对这种共识结果的跨链，还必然会实现共识过程甚至共识机制本身的跨链。在这个基础上，目前构建在单一区块链上的各种DApp（Decentralized Application，去中心化应用），未来也一定会原生地构建在多条区块链上。这种原生多链DApp 不仅能够集成目前的跨链机制所实现的对不同链上共识结果的跨链，而且能直接完成对不同链
上共识过程甚至共识机制的跨链。就像我们现在编写代码，直接通过网络编程，甚至直接进行云原生编程，而不像20 年前，连最基本的用于节点通信的socket 函数都要自己来实现。
编者将这种原生地构建在多条区块链上的DApp 命名为原生多链DApp，将大多数区块链、基于去中心化机制实现的多条区块链间的原生跨链，以及不同链上的去中心化扩展和原生多链DApp 命名为Web 3.1。将来也许还会有Web 3.2、Web 3.3，甚至Web 3.9，未来对于去中心化领域的发展，我们只能拭目以待了。
目前Web 3 的发展面临着用户隐私保护不足、系统可扩展性差、信任受共识机制的主权区域限制、Web 3 与非Web 3 难以可靠可信连通等种种问题。因此，在确保链上数据公开、透明、不可篡改的同时，如何保护用户隐私、不同的扩展方案如何可信地传递数据、不同共识机制所形成的主权区域如何可信地扩展和传递共识，以及Web 3 系统如
何与非Web 3 系统可信地交换数据和信用，都是Web 3 发展必须面对和亟待解决的问题。
4. 零知识证明为Web 3 和元宇宙的发展提供了新的可能
针对Web 3 发展面临的问题，业界虽然提出了多种方案，但这些方案大都存在比较严重的缺陷，如大多数方案都需要引入一个中心化或去中心化的第三方，这无疑带来了更大的信任问题。零知识证明为解决Web 3 发展面临的问题带来了新的思路，零知识证明的一些解决方案也在Web 3 相关领域有了比较成功的实践。
如果说区块链在去中心化的基础上实现了去身份信任，那么零知识证明就直接实现了去信任。证明者生成的零知识证明只要能通过验证，我们就基本可以确定被零知识证明验证过的事件是可信的。零知识证明并不是严格的数学证明，而是概率证明。虽然从理论上讲，证明者有可能成功欺骗验证者，使得验证者相信证明者拥有或具备某种知识，但如果经过多次零知识证明验证，证明者仍然能够成功欺骗验证者的概率将会越来越低，以至不可能。
零知识证明尽管有很多优点，但很难直接使用。零知识证明和其他隐私计算方案一样，都需要进行构造。如何构造零知识证明，使其既与当前的计算问题相匹配，具有一定的通用性，又不消耗过多的计算资源，还要确保有效性，是零知识证明被广泛应用面临的重要挑战。
前文说过，Web 3 的发展是投机力量和创新力量综合驱动的。在Web 3 几乎全面开源的背景下，在各种投机力量和创新力量的驱动下，零知识证明在Web 3 领域的发展速度远快于Web 2。零知识证明当前阶段最多的应用创新还是在Web 3 领域的创新，因此我们也把关注点更多地投向了Web 3 领域。
我们也需要对零知识证明在其他非Web 3 领域的应用保持高度关注。因为在编者看来，Web 2 与Web 3 是网络发展和业务组织的两个不同方向，Web 3 不是对Web 2 的替代，两者分别对应了人类社会中业务的两种不同的组织方式。Web 2 采用了中心化的业务组织方式，保持了中心化一贯的效率高的优点，但存在一定的信任成本；Web 3 则采用了去中心化的业务组织方式，信任基础强，但在单点上效率低。2022 年6 月11 日，推特创始人Jack Dorsey 在Consensus 大会上宣布将构建Web 5 去中心化网络平台，直接取代目前Web 2 和Web 3 的概念，因此也被称为“Web 2+ Web 3= Web 5”。编者对此是比较认可的，即未来的元宇宙或第三代互联网，一定是兼容Web 2 与Web 3 的，同时，Web 2 与Web 3 也一定是要有交互的。那么，如何在两套不同的共识和机制之间实现可信连接呢？
至少目前来看，零知识证明是一套可行的方案。因此，我们也可以预期，零知识证明在推动Web 3 继续发展的同时，也将深度推动Web 2 和Web 3 的融合，进而推动整个元宇宙的发展。
5. 关于本书
基于当前Web 3 世界的快速发展，零知识证明在落地应用方面取得的快速进展及其在Web 3 中应用的迅速推广和普及，以及零知识证明和Web 3 未来广阔的发展前景，编者从技术原理和相关具体工程实现的角度编写了《Web 3 中的零知识证明》一书。本书定位为科普读物，面向的读者包括但不限于Web 3 领域的从业者、对零知识证明感兴趣的学生及业内人士。
本书第1 章从总体上回顾了Web 3 的发展，以及当前的表现形态，第2 章和第3 章从最简洁的数学层面向读者介绍了零知识证明是什么，以及如何构建零知识证明。第4章从技术层面介绍了Web 3 世界中零知识证明的主流实现方案，第5 章从应用层面介绍了零知识证明在Web 3 世界中的一些典型应用，第6 章介绍了零知识证明在其他领域的
应用及展望。
虽然在第3 章和第4 章，为了说明零知识证明系统是如何构建的，编者不得不引入一些数学知识，但这些数学知识也是零知识证明最基本的内容，只要读者静下心来学习，必要时再借助一些其他渠道的资源，就还是能够掌握的。当然，如果觉得第3 章和第4章关于数学知识的部分有难度，也完全可以跳过，更多关注零知识证明在Web 3 及Web 3 领域之外的一些应用。当然，这些应用都是目前市面上真实存在且正在发生的项目。随着更多应用的发展和人类数字化进程的进一步深化，零知识证明的应用领域会越来越广，人类对零知识证明的需求也会越来越多，零知识证明将发挥更多、更大的作用。
为简洁起见，除非特殊标明，本书不再区分Web 3 和 Web 3.0，尽管对这两者如何界定都快成为业界“公案”了，本书也不再区分 Web 2 和 Web 2.0，一律以Web 3 和Web 2 统一指代。
此外，由于零知识证明和Web 3 都处于行业发展初期，绝大多数项目也是“草根”创业类项目，这个领域又秉持去中心化的原教旨理念，缺少行业协会等相关组织的规范，因此很多表述相当不规范，包括英文缩写中的大小写、连字符“-”的使用等。即使同一个词语，不同公司和项目也有不同的表达，甚至同一个公司和项目对同一个词语在不同地方也会有不同的表述。本书在不改变原有项目和应用表述的情况下，已经尽可能让其保持一致，但限于本书的规模以及包括的项目数量众多，还是难以完全统一。特此说明。
高承实
2023 年12 月

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