To: bitcoin-dev@lists.linuxfoundation.org
From: Max Hillebrand <max@towardsliberty.com>
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Message-ID: <96dc101e-30ba-9833-7ba0-41eda910d3cc@towardsliberty.com>
Date: Wed, 15 Jan 2020 22:23:15 +0100
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Subject: [bitcoin-dev] ***UNCHECKED*** Wormhole: Sending and receiving
	bitcoin anonymously
Precedence: list


-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA512


Hello all!

May I propose you this protocol which seemingly provides a great level
of privacy for both the sender and receiver of bitcoin. This was
initially posted to the [Wasabi Wallet
GitHub](https://github.com/zkSNACKs/Meta/issues/64), and after thorough
contemplation and minor tweaks, I would now like to request your
feedback on the conceptual design and possible implementation.

Cheers
Max


# Wormhole


## Abstract

A protocol to transfer bitcoin, without the receiver gaining knowledge
of the input of the sender, and without the sender gaining knowledge of
the output of the receiver, while simultaneously generating equal value
CoinJoin outputs with anonymity set.


## Introduction

This is achieved by minor changes to the [Zero
Link](https://github.com/nopara73/zerolink) CoinJoin protocol, utilizing
a centralized coordinator who cannot steal, and cannot spy. Schnorr
blind signatures are used to obfuscate the link between inputs and equal
value outputs throughout the ceremony. The coordinator does not gain
knowledge that Wormhole is used.


## Protocol

- - Alice A [with tor identity A1 and A2] has a 5.5 bitcoin UTXO
- - A sends 1 bitcoin to Bob B [with tor identity B1 and B2]
- - Wasabi server W coordinates the zero link CoinJoin:
=C2=A0=C2=A0=C2=A0 -- Equal value denominations are 1, 2, 4, 8, 16, 32 bi=
tcoin
=C2=A0=C2=A0=C2=A0 -- Anonymity set for each denomination is 100
=C2=A0=C2=A0=C2=A0 -- Wormhole protocol is opt-in for some unknown number=
 of peers

### Input Registration

- - A generates an input proof of the 5.5 bitcoin UTXO
- - A generates one `blindedOutput` with 4 bitcoin, and one
`changeAddress` with 0.5 bitcoin
- - B generates one `blindedOutput` with 1 bitcoin & he sends this
to A
- - A1 sends all of the above to W
- - W verifies
=C2=A0=C2=A0=C2=A0 -- `maxInputsPerRegistraion` not reached
=C2=A0=C2=A0=C2=A0 -- `maxInputPerTx` not reached
=C2=A0=C2=A0=C2=A0 -- `blindedOutput` never registered
=C2=A0=C2=A0=C2=A0 -- each input
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 --- not already registered for=
 this round
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 --- UTXO not banned
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 --- proof
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 --- unspent
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 --- if coinbase, confirmations=
 > 100
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 --- must be SegWit v0 [maybe a=
lso v1] bech32
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 --- is from unconfirmed CoinJo=
in tx
- - W generates `uniqueID`
- - W signs all `blindedOutput`
- - W sends `uniqueID` & `signedBlindedOutput` to A1

### Connection Confirmation

- - Starts when `timeSinceLastRound > maxWaitPeriod` OR
`registeredInputs > requiredInputs`
- - A abandons if confirmation is refused
- - A1 sends `uniqueID` W
- - W verifies `uniqueID`, and calculates `roundHash =3D hash of all
registered inputs`
- - W sends `roundHash` to A1 and B1

### Output Registration

- - Starts when `confirmedUniquelds =3D=3D registeredInputs` OR `timeout =
&&
confirmedUniquelds >=3D requiredInputs`
- - A sends `signedBlindedOuput_B` to B
- - Both A and B unblind the `signedBlindedOutput`
- - Both A2 and B2 send `output` & `signature` & `roundHash`
**DIRECTLY** to W - they do **NOT** send to each other
- - W verifies `roundHash` & `signature` & `Output`

### Signing

- - Starts when `outputs =3D=3D registeredInputs` OR `timeout` [go signin=
g,
even if there are missing outputs to identify them and ban them as they
won't sign]
- - W builds CoinJoin transaction `CJTX` and sends to A1 and B1
and all other peers
- - A and B verify `roundHash` [by calculating hash of all `txInputs`]
- - B verifies that his output is included & signs a commitment
message m where he acknowledges that it is included & sends m to A
- - A verifies that her input and her outputs are included & verifies
B signature of m [assumption that Bob provides a correct address, as
with any transaction] & signs `CJTX`
- - A1 sends `uniqueID` & `signature, inputIndex` to W - A does
**NOT** send this to B
- - W verifies `uniqueID` & each signature against
`inputs[uniqueID][index]`

### Broadcast TX

- - Starts when `signatures =3D=3D registeredInputs`
- - W broadcasts signed transaction to the Bitcoin peer-to-peer network


## Result

- - A has one 4 bitcoin UTXO with 100 anonset & one 0.5 bitcoin
UTXO with 1 anonset
- - B has one 1 bitcoin UTXO with 100 anonset
- - W knows the input and change of A & W does not know who
controls which equal value output & W does not know that B has no inputs
- - A does not know the output of B, there are 99 possible coins.
- - B does not know the input and outputs of A, there are 100+
possible coins.


## Communication

This is an interactive protocol with several rounds of communication,
thus all A & B & W need to be online. The communication between
A and B can be done on any suitably private channel, including but
not limited to tor, QR codes, SD cards, or carrier pigeon. The
communication between A / B & W will be the same as used for the
regular zero link implementation, most likely tor.


## Privacy

The equal value zero link outputs from A and B have the anonymity
set of the total number of equal value zero link outputs in the same
transaction. Wormhole breaks the assumption that zero link is a
consolidation within the same wallet [`Input Alice =3D Output Alice +
Fee`], in a way that neither A nor B can spy on each other. W does
not know if any peer is using Wormhole, none or one or all peers
**might** use it.


## Questions

I am not sure what information is broadcasted from W to all peers in
the round, and if Bob can get this information without revealing that he
is the receiver of a Wormhole transaction [he has no input proof]. What
information can be send from W to B directly will determine the
trust level of A passing honest messages.

Wormhole might be used in conjunction with [Pay to
Endpoint](https://medium.com/@nopara73/pay-to-endpoint-56eb05d3cac6) or
[Knapsack](https://www.comsys.rwth-aachen.de/fileadmin/papers/2017/2017-m=
aurer-trustcom-coinjoin.pdf)
so that A can send a specific amount to B, with part being the equal
value zero link output, and part the P2EP change, or Knapsack
sub-transaction.

[Atomic coin
swaps](https://github.com/ElementsProject/scriptless-scripts/blob/master/=
md/atomic-swap.md)
with Schnorr adaptor signatures might be integrated, so A input in
`CJTX1` "pays" B output in `CJTX2`, but this might require B to know
the signature [and thus the input] of A.

- --=20
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