📜 [專欄新文章] Tornado Cash 實例解析

✍️ Johnson

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Tornado Cash 是一個使用 zk-SNARKs 建立的 Dapp，它實現了匿名的代幣交易，這篇文章就用一些程式碼片段，來分享它是怎麼運作的。

本文為 Tornado Cash 研究系列的 Part 3，本系列以 tornado-core 為教材，學習開發 ZKP 的應用，另兩篇為：

Part 1：Merkle Tree in JavaScript

Part 2：ZKP 與智能合約的開發入門

Special thanks to C.C. Liang for review and enlightenment.

我們知道在以太坊上的交易紀錄都是公開的，你可以在 etherscan 上看到某個地址的所有歷史交易紀錄，當然地址是合約的話也是一樣。

也許創建一個新的錢包和地址就好了？假設一個情境是 Alice 想要匿名傳送 1 ETH 給 Bob，Alice 原本的錢包是 A，但她不想讓 A 地址傳給 Bob 的交易紀錄被看到，所以 Alice 創建另一個錢包 B，顯然 B 錢包是空的，Alice 必須把 A 錢包的 1 ETH 傳到 B 錢包，再用 B 錢包的地址傳給 Bob。

但問題就在於，只要追蹤 B 錢包的地址，就能看到 B 的歷史交易紀錄中 A 錢包曾經打幣給 B 錢包，於是到頭來交易還是被追蹤到了。

Tornado Cash 的解決方案，簡單來說，它是一份合約，當你要匿名傳送代幣時，就把一定數量的幣丟進合約裡 (Deposit)，此時你會拿到一個 note，長得像這樣：

tornado-eth-0.1-5-0x3863c2e16abc85d72b64d78c68fca5936db2501832e26345226efdfb2bc45804977f167d86b711bb6b4095ddaa646ec93f0a93ac4884a66c1d881f4fc985

note 就是一串字串，擁有這字串的人，就能提領 (Withdraw) 剛剛傳入合約的代幣。握有 note 就代表擁有提款的權利，所以 note 一旦被別人知道，別人就可以把錢給提走。

其中，後面那段亂碼，本篇文章就以「秘密」來稱呼，這個秘密是由 secret 與 nullifier 組成，而這兩個都是在鏈下隨機產生的亂數。

因此 Tornado 的合約基本上會有兩個函式：

Deposit

Withdraw

有興趣的人可以先到 Dapp 上先玩一次看看，使用 Goerli 測試網，這裡可以領 Goerli 的代幣：https://goerli-faucet.slock.it/

Deposit

我們就從 Deposit 開始說起，簡單來說， Deposit 是將資料儲存到合約的 Merkle Tree 上。

剛剛提到的秘密，它是在鏈下產生，由 secret 跟 nullifier 組成，合在一起之後也稱作 preimage，因為我們要對這個 preimage 進行 hash，就會成為 commitment。

合約中 Deposit 如下：

deposit 除了傳送代幣到合約之外，需填入一個參數 _commitment。

我們對 preimage 使用 Pedersen 作為 hash function 加密後產生 commitment，以偽代碼表示如下：

const preimage = secret + nullifier;const commitment = pedersenHash(preimage);

這個 commitment 會成為 Merkle Tree 的葉子，所以合約中的 _insert(commitment) 來自 MerkleTreeWithHistory.sol 的合約，將我們的資料插入 Merkle Tree，然後回傳一個 index 給你，告訴你這個 commitment 在 Merkle Tree 上的位置，最後一起發布成公開的 Deposit 事件。

我們知道 MerkleTree 是將一大筆資料兩兩做雜湊後產生一個唯一值 root，這個 root 就是合約上所儲存的歷史資料。

root 的特性就是只要底下的資料一有更動，就會重新產生新的 root。

所以只要一有用戶 deposit ，就會插入新的葉子到 Merkle Tree 上，於是就會產生新的 root，所以在合約中有一個陣列是用來儲存所有的 root 的 roots：

bytes32[ROOT_HISTORY_SIZE] public roots;

roots 是用來紀錄每個 deposit 的歷史，每一次 deposit 都會創造新的 root，而所有 root 都會被儲存進 roots 裡，於是當你要提領的時候，就要證明你的 commitment 所算出的 root 曾經出現在 roots 裡，代表曾經有 deposit 的動作，因此才可以進行提領。

Withdraw

在 Deposit 之前 Tornado Cash 就會在鏈下產生秘密後交給使用者，擁有這個秘密的人等於擁有提款的權利。

提領的時候，秘密會在鏈下計算後產生 proof，proof 是 withdraw 需要的參數，所以只要確保這個 proof 能夠被驗證，那麼代幣的接收地址 (recipient) 就可以隨便我們填，只要不填上當初拿來 deposit 用的地址，基本上就做到匿名交易的效果了。

也就是說，產生這個 proof 並提交給合約，能夠證明此人知道秘密，但卻不告訴合約秘密本身是什麼。

function withdraw(bytes calldata _proof, bytes32 _root, bytes32 _nullifierHash, address payable _recipient, address payable _relayer, uint256 _fee, uint256 _refund) external payable nonReentrant;

我們可以清楚看到 withdraw 函式裡沒有接收有關秘密的任何資訊作為參數，也就是秘密不會與合約有所接觸，也不會暴露在 etherscan 上。

回顧 ZKP 所帶來的效果：

鏈下計算

隱藏秘密

在 Tornado Cash 的例子中，我們用秘密來產生證明，完成的鏈下計算包括：

將秘密 hash 成 commitment

算出 Merkle Tree 的 root。

以下是簡化後的 withdraw.circom：

template Withdraw(levels) { signal input root; signal input nullifierHash;

signal private input nullifier; signal private input secret; signal private input pathElements[levels]; signal private input pathIndices[levels];

component hasher = CommitmentHasher(); // Pedersen hasher.nullifier <== nullifier; hasher.secret <== secret; hasher.nullifierHash === nullifierHash;

component tree = MerkleTreeChecker(levels); // MiMC tree.leaf <== hasher.commitment; tree.root <== root; for (var i = 0; i < levels; i++) { tree.pathElements[i] <== pathElements[i]; tree.pathIndices[i] <== pathIndices[i]; }}

component main = Withdraw(20);

從上述代碼就可以看出這份 circuit 的 private 變數有：

secret

nullifier

pathElements

pathIndices

而 public 變數有：

root

nullifierHash

如同我們一開始說過的，秘密就是指 secret 與 nullifier。這裡進行的鏈下計算就是對 secret 與 nullifier 雜湊成 commitment。而使用的 hash function 叫做 Pedersen。

在進行 Merkle Tree 的計算之前，我們還檢查了 nullifier 雜湊後的 nullifierHash 跟 public 變數 nullifierHash 是不是一樣的。

hasher.nullifierHash === nullifierHash;

接下來，開始計算 Merkle Proof，用意是確認經過雜湊後的 commitment 有沒有出現在 Merkle Tree 上，所以我們的 private input 還有 pathElements 與 pathIndices（詳情參考 Part 1 Merkle Tree in JavaScript），讓它跑一趟 Merkle Proof 的計算，最後就能夠算出一個 root，再確認計算後的 root 與我們的 public 變數 root 是否一樣。

tree.root <== root;

於是我們就能產生一個 ZKP 的證明 — 證明 private 變數：secret, nullifier, pathElements, pathIndices 可以計算出 public 變數：root 與 nullifierHash。

把這個證明提交給合約，合約透過 Verifier 驗證 proof 是否正確，以及必須事先確認：

public 變數 root 有在合約的 roots 裡面。

public 變數 nullifierHash 在合約中是第一次出現。

以下附上完整的 withdraw 原始碼：

必須注意 ZKP 是向合約證明使用者填入的 secret 和 nullifier 可以計算出某個 root，但無法保證這個 root 曾經在合約的 roots 歷史上。

所以合約的 withdraw 中，除了 verifyProof 之外，還要事先檢查 ZKP 算出來的 root 是不是真的在歷史上發生過，所以需要 isKnownRoot 的檢查：

function isKnownRoot(bytes32 _root) public view returns(bool)

必須先檢查 isKnownRoot 後才能進行 verifyProof。

經過 verifyProof 驗證成功後，合約就開始進行提款的動作，也就會將代幣傳到 recipient 的地址，最後拋出 Withdrawal 的事件。

nullifier 與 nullifierHash

為什麼我們的秘密不是只有 secret 還要額外加一個 nullifier？

簡單來說，這是為了防止已經提領過的 note 又再提領一次，也就是所謂的 double spend。

require(!nullifierHashes[_nullifierHash], "The note has been already spent");

可以看到 withdraw 需要填入參數 nullifierHash，跟 isKnownRoot 一樣的狀況，我們需要對電路的 public 變數先經過一層檢查之後，才能帶入到 verifyProof 裡面。

nullifierHash 可以理解為這個 note 的 id，但它不會連結到 deposit，因此可以用來紀錄這個 note 是否已經被提領過。

所以當 verifyProof 驗證成功之後，我們要紀錄 nullifierHash 已完成提領：

nullifierHashes[_nullifierHash] = true;

有關為什麼需要事先檢查 public 變數後，才能帶入 verifyProof ，可以參考 Part 2：ZKP 與智能合約的開發入門 提到的 publicSignals 的部分。

附上 Tornado Cash 的架構圖：

簡化版的 tornado-core

tornado-core 的程式碼很簡潔漂亮，所以我模仿該專案自己實作一遍：

simple-tornado：https://github.com/chnejohnson/simple-tornado

這份專案只完成了 tornado-core 的核心部分，不一樣的是我的開發環境使用 hardhat 與 ethers 寫成，而 circom 與 snarkjs 使用官方當前的版本，合約用 0.7.0，測試使用 Typescript 。

比起兩年前的 tornado-core ，simple-tornado 使用的技術更新，可能更適合初學者理解這份專案，但是它有 bug…我在 issues 的地方有紀錄說明。

在開發的過程中，我的順序是先從最小單位的 MiMC hash function 開始玩，發現必須 javascript 算一次 hash、solidity 算一次、circom 再算一次，確保這三個語言對同一個值算出同樣的 hash 之後，才能放心去做更複雜的 Merkle Tree。

總結

我們可以看到 Tornado Cash 簡單的兩個函式：Deposit 與 Withdraw，透過將代幣送入合約後再提領到另一個地址的流程，應用 ZKP 達成匿名的交易。

除了斷開 Deposit 與 Withdraw 的地址關聯性之外，Tornado Cash 還有做了一層「藏樹於林」的隱私防護，這部份的解釋就請參考 ZKP 讀書會 Tornado Cash。

網路上很多關於 ZKP 的文章或專案都是在 2019 年後出產的，經過許多人對這項技術的嘗試，讓我們對 ZKP 有了更清晰的理解，如今兩年後，開發工具也變得更加成熟，期待未來在 web 隱私議題上能看到更多 ZKP 大放異彩的應用。

原始碼

tornado-core

simple-tornado

參考資料

ZKP 讀書會 Tornado Cash

Tornado Privacy Solution Cryptographic Review

Tornado Cash 實例解析 was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

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📜 [專欄新文章] Using MPC to Help Achieve Blockchain Privacy

✍️ Yahsin Huang

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

This post answers some of the most commonly asked questions about using multi-party computation (MPC) in blockchains.

What is MPC?

Multi-party computation (MPC) is a cryptographic protocol that does a joint computation involving multiple parties over their inputs while keeping those inputs private.

A famous example of MPC is Yao’s Millionaires Problem. Two millionaires want to know who is richer without finding out information about each other’s actual wealth. Naively they can simply tell their wealth to a third party. Then the third party compares their wealth and lets them know who is richer. But then this option is undesirable because the third party learns the information of their wealth.

The challenge of Yao’s Millionaires Problem is the computation wouldn’t be able to have a result without the two parties’ private information. To get the end result, you need those information involved in the computation. But at the same time, you are not allowed to reveal those private information to the party who performs the computation. That’s the main problem that MPC wants to solve.

Why it matters in blockchain?

In the real world, not everyone’s a millionaire. Not everybody wishes to compare their assets and wealth with others. In the blockchain space, there’s a need to ensure the inputs are shielded from multiple parties for privacy purposes; hence, the need for MPC protocols.

If we look at the current landscape of the blockchain world, notice there are blockchains doing great for programmability, such as Ethereum blockchain, allowing developers to build great tools and applications on top of them. There are also blockchains doing great for privacy, such as ZCash blockchain, allowing users to send transactions in a privacy-preserving way.

However, there’s a lack of blockchains that are designed for maximum programmability with maximum privacy. That’s why a lot of folks are pushing forward the work on incorporating MPC protocols into blockchain designs.

Why ZK is not enough?

Zero Knowledge Proofs (ZKP) is great at shielding private information that involves only one party. ZKP alone cannot be applied to provide privacy in multiple-party settings, such as auctions or in the case of Yao’s Millionaires Problem. In those settings, computations would involve private inputs from multiple parties, and so ZKP wouldn’t be enough. We would need to turn to MPC to achieve that.

Recent developments in MPC

In his presentation “MPC as a Blockchain Confidentiality Layer,” Miller gave a high-level overview of how MPC can be viewed as a confidentiality layer for blockchains as illustrated in the slide. Credit: https://youtu.be/0VuBELYfChM

How does MPC work with blockchains?

HoneyBadgerMPC builds a sidechain that performs MPC protocol computation. The sidechain acts as a confidentiality layer to the public blockchain, where secret data is stored.

How can developers build MPC applications?

Developers are able to develop MPC applications with Ratel language. Writing Ratel feels very similar to writing Solidity contracts. The compiler compiles Ratel code into two parts: the Ethereum part, and the MPC as a sidechain part.

Ratel code looks like this: https://github.com/initc3/HoneyBadgerSwap/blob/coconut/ratel/trade.rl

Learn more about MPC as a sidechain

One of the biggest news this past month was you could now play with HoneyBadgerSwap’s demo website. HoneyBadgerSwap is basically a dark pool version of Uniswap using MPC. You will need some Kovan ETH to test it out. Yunqi Li (UIUC, IC3) made a great Medium story about HoneyBadgerSwap. Read it here: “HoneyBadgerSwap: Making MPC as a Sidechain,” published on April 22, 2021.

Watch a really great talk by Andrew Miller “MPC as a Blockchain Confidentiality Layer,” presented at the IC3 Blockchain Camp 2020, to understand the HoneyBadgerMPC protocol more.

If you are someone who would like to delve into the topic with textbooks, be sure to add the book “A Pragmatic Introduction to Secure Multi-Party Computation” to your reading list. The content is available in PDF.

Using MPC to Help Achieve Blockchain Privacy was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

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Almost every Christmas, my family and I spend our holiday watching movies.

A particular favorite is Die Hard, the iconic Bruce Willis film that sees the Hollywood tough guy rescue hundreds of hostages from a skyscraper taken over by terrorists.

Not an entirely believable film, but fun. It has some great one-liners.

Usually this holiday movie watching time is quite fun, except for when someone wants to see a film with technology in it.

When it comes to some movies, any time they show tech, they almost invariably get it wrong. Someone, usually me, starts yelling at the screen... "That CANNOT happen!" or "Seriously?!?"

It kind of takes the nog out of the egg nog, if you know what I mean.

There are some movies that actually get technology right, however. Here is a list of them.

Movies That Actually Got Tech Right: https://au.pcmag.com/features/52972/10-movies-that-actually-got-technology-right

But what I'd really like to show you is a personal favorite tech-themed movie, because of what it teaches us about the founder mindset and serendipity. I always like to say that the founder's mind is planned luck.

In "The Imitation Game," we see this clearly.

"The Imitation Game" is the depiction of how Alan Turing and fellow computer scientists broke the cryptographic code that the Nazis were using to send their war plans to each other. This discovery helped end the war and saved Britain and the rest of the world from unimaginable suffering.

What I think this gets right is that as a founder -- or a discoverer or adventurer -- you have to put in a lot of demanding work, and personal sacrifice, to prepare your mind and your product or startup for the simple and elegant answer that makes it work.

You cannot just think the answer into existence.

You have to create a framework.

You have to suffer through the empirical search and discovery.

You have to experiment.

You have to fail at it.

You have to personally go through hell.

In order to....

Achieve an answer that is simple because you created the framework to see it simply.

This Christmas, I leave you with this video clip of the moment that Turing cracks the code. What he relied on to reach that magic moment seemed so stunningly obvious.

But had he not done all the legwork, it would have never mattered.

Merry Christmas

https://youtu.be/zZuqLLdx2YQ

Doug Crets, English Communications Master
AppWorks

CItation/references :
Carter, J. L., & Wegman, M. N. (April 1979). Universal classes of hash functions. Journal of computer and system sciences, 18(2), 143-154.

Buer, M. L. (23 February, 2010). U.S. Patent No. 7,669,234. Washington, DC: U.S. Patent and Trademark Office.

Antonio Madeira (13 March, 2019) “How Does a Hashing Algorithm Work?”
https://www.cryptocompare.com/coins/guides/how-does-a-hashing-algorithm-work/

Daniel (14 AUGUST, 2018)” Cryptographic Hash Functions Explained: A Beginner’s Guide”
https://komodoplatform.com/cryptographic-hash-function/

Tim Fisher (07 January, 2019)” Can Cryptographic Hash Functions Be Reversed?”
https://www.lifewire.com/cryptographic-hash-function-2625832