Taprootized Atomic Swaps

Taprootized Atomic Swaps (TAS) is an extension for Atomic Swaps that presumes the untraceability of transactions related to a particular swap. Based on Schnorr signatures, Taproot technology, and zero-knowledge proofs, the taprootized atomic swaps hide swap transactions under regular payments.

Intro

Atomic swap is an incredible approach to cross-chain exchanges without mediators. However, one of the disadvantages of its implementation in the classical form is the “digital trail” — any party can make a matching between transactions in the blockchains in which the exchange took place and find out both the participants in the exchange and the proportion in which assets were exchanged.

On the other hand, atomic swaps is a technology that initially assumed the involvement of only two parties and a “mathematical contract” between them directly. That is, an ideal exchange presupposes 2 conditions:

1. Only counterparties participate in the exchange (works by default)
2. Only counterparties know about the fact of the exchange (it would be nice to ensure)

This paper will provide a concept of taprootized atomic swaps that allow hiding the swap's very fact. To an external auditor, transactions to initiate and execute atomic swaps will be indistinguishable from regular Bitcoin payments. In the other accounting system involved in the transfer, more information is disclosed (the fact of exchange can be traced). Still, it is impossible to link this to the corresponding Bitcoin transactions (without additional context from the involved parties).

The protocol includes the following steps:

1. Alice (skA, PKA) and Bob (skB, PKB) have their keypairs and know each other's public keys.
2. Alice generates a random k and calculates the public value K = k * G
3. Alice forms the alternative spending path Script = sig(skA) + Locktime in the form of Bitcoin Script
4. Alice calculates an escrow public key as PKEsc = K + PKB + hash((K + PKB) || Script) * G (here, escrow is just a public key, formed using Taproot technology
   1. The signature sig(skEsc), verified by thr PKEsc, can be generated only with the knowledge of k, skB and Script
5. Alice calculates the h as a hash value of k (zk-friendly hash function is recommended to use)
6. Alice forms the funding transactions with the following conditions of how it can be spent:
   1. Signature of skEsc: Bob, with knowledge of k and skB can spend the output
   2. Signature of skA + Locktime: Alice, with knowledge of skA can spend the output, but only after some point in time t1 (it's the Script itself)
7. Alice sends the transaction to the Bitcoin network
8. Alice generates the zero-knowledge proof that includes:
   1. The proof of knowledge of k that satisfies k * G == K
   2. The proof of knowledge of k that satisfies zkHash(k) == h
9. Alice provides the set of data to Bob:
   1. h
   2. K
   3. Script
   4. proof
10. Bob calculates PKEsc as K + PKB + hash((K + PKB) || Script) * G and finds the transaction locked BTC (verifies it exists). Then Bob performs the following verification:
    1. Verifies that Alice knows k that satisfies k*G == K and zkHash(k) == h, it means that Bob can access the output PKEsc if he receives k
    2. Verifies that the Script is correct and includes only the required alternative path.
11. If verifications are passed, Bob forms the transaction that locks his funds on the following conditions:
    1. Publishing of k and the signature of skA: only Alice can spend it if she reveals k (hash preimage)
    2. Signature of skB + Locktime: Bob, with knowledge of skB, can spend the output, but only after some point in time t2
12. Bob sends the transaction to the Ethereum network (or any other that supports zkHash())
13. Alice sees the locking conditions defined by Bob and publishes the k together with the signature generated by her skA. As a result - Alice spent funds locked by Bob.
    1. If Alice doesn’t publish the relevant k, Bob can return funds after locktime is reached
14. If Alice publishes a transaction with k, Bob can recognize it and extract the k value
15. Bob calculate the needed skEsc as skEsc = k + skB + hash((K + PKB) || Script)
16. Bob sends the transaction with the signature generated by the skEsc and spends funds locked by Alice.

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The first taprootized atomic swap between Bitcoin and Ethereum mainnets

Transactions:

1. Alice locks BTC: 850e9258bf8b3bb280d32a647198d8024aece543dc283f7bfa526f4c0ceb1ab8
2. Bob locks ETH: 723919c0e8ec57d38792ec29b2cb82ee885b9fbbc886b34ff40fb5d3f7cc9b43
3. Alice withdraws ETH from the contract: 47546191a7c99ec4a7ddc243d6ea75d345ab3aff0762e09dd2f537731bd484f3
4. Bob spends BTC: 859dbfaa901d7106aecc8cb29966ede0c9d7a17c2cae31f4d420c1d770e9706d

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A bit about the repository

This repository provides all components for executing an atomic swap, including a script for an Ethereum-Bitcoin exchange between Alice and Bob.

• circuits: Contains Circom circuits for Zero-Knowledge proof creation in step eight of the outlined flow. These circuits verify the knowledge of a private 256-bit scalar k, where K = k * G and h = Poseidon(k), with K and h being public, Poseidon being the hash function, and G representing the Secp256k1 base point.
• contracts: Contains the Depositor contract in Solidity designed for depositing native currency using a 256-bit number h and locktime, locking funds with two withdrawal conditions:
  • Spender knows some k that h = Poseidon(k)- money goes to the message sender
  • locktime has passed - money goes to the deposit maker
• crates: Contains Rust crates for ZkSnark witness, proof generation, and validation. Proof generation currently takes about 13 seconds on an M1 Pro chip, with witness calculation accounting for 10 seconds. Utilizing c++ bindings instead of the existing wasm witness calculator can notably reduce this time.
• src: Contains the Rust script for facilitating an atomic swap between Alice and Bob. It encompasses all steps outlined in the documentation, including proof generation, taproot transaction creation, and executing transactions on both Bitcoin and Ethereum networks.
• scripts: Contains auxiliary scripts for Circom and SnarkJS.

How to try it out?

You can use either testnets for Ethereum and Bitcoin networks or run the local test networks by using such utilities as ganache for Ethereum and nigiri for Bitcoin.

You can use this deployed, verified and ready for use contracts:

• Ethereum mainnet: 0x936f971455bc674F77312f451963681fe964E838
• Sepolia testnet: 0x85BEaB7f80B375175BeCC3f68Bf86d33099fD576

You can use trusted setup files (.ptau, at least 17th power) from [SnarkJs] repository, you can find it in the readme section, for ZK proof generation.

Steps:

0. Install Cargo, Circom, SnarkJS
1. Setup config.toml. Check the config.example.toml for example, it has detailed description.
2. Compile & run the script with a provided config path (because of the outdated packages, it can't be compiled in release mode as well as using cargo install):

   cargo run config.toml

Build for Linux

Before compiling make sure, that you have the OpenMP installed on your device. It is required dependency to build the rapidsnark-sys crate.

sudo apt update sudo apt upgrade
sudo apt install libomp-dev

Acknowledgments

We use a circom ecdsa implementation from 0xPARC.