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From: Bryan Bishop <kanzure@gmail.com>
Date: Wed, 7 Aug 2019 08:48:06 -0500
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To: Bitcoin Dev <bitcoin-dev@lists.linuxfoundation.org>,
	Bryan Bishop <kanzure@gmail.com>
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Subject: [bitcoin-dev] Bitcoin vaults with anti-theft recovery/clawback
	mechanisms
Precedence: list

Hi,

I have a proposal for implementing bitcoin vaults in a way that does not
require any soft-forks or other software upgrades, although it could benefit
from SIGHASH_NOINPUT which I'll describe later.

I call them pre-signed vaults.

Vault definition
================

Here, a vault is defined as a transaction setup scheme that binds both the user
and the attacker to always using a public observation and delay period before a
weakly-secured hot key is allowed to arbitrarily spend coins. This is the same
definition previously used[1]. During the delay period, there is an opportunity
to initiate recovery/clawback which can either trigger deeper cold storage
parameters or at least reset the delay period to start over again for the same
keys.

One of the important components of this is the delete-the-key pre-signed
transaction concept, where only a single transaction is (pre)signed before
deleting the key. This is basically an emulation of a covenant and enforces a
certain outcome.

Background and motivation
=========================

I was looking at Eyal and Sirer's 2016 vaults paper [1], and I saw this
headscratcher:

> Vault transactions use a delay mechanism. We note that vault transactions
> cannot be implemented with existing timing mechanisms such as
> CHECKLOCKTIMEVERIFY opcode or transaction locktime.

This was probably written before the introduction of OP_CHECKSEQUENCEVERIFY.
Still, a viable construction would have more steps than just using OP_CSV. They
were probably not thinking about what those steps might be, because in the
context of the paper they were proposing a bitcoin vault implemented using
recursive consensus-enforced covenants via a new opcode, which obviously cannot
be deployed without an upgrade fork. Covenants have been discussed for years,
but require new opcodes or other consensus-enforcement changes.

Relative locktimes are useful here because there is no knowledge as to when the
transactions might be broadcasted in the future. The delays need to be relative
to after the transaction is included in the blockchain, not to setup
initialization time.

Also, from [2]:

> We show that a [vault transaction] mechanism is currently not possible in all
> cryptocurrencies [...] Bitcoin's scripting language requires support for
> covenants.

I haven't seen any previous proposal for how to implement recursive bitcoin
vaults without a fork and without a covenant. After asking around, I am pretty
sure this is somewhat novel. The closest I guess is [3].

Vaults are particularly interesting as a bitcoin cold storage security
mechanism because they enable a publicly observable delay period during which
time a user could be alerted by a watchtower that a thief might be in the
process of stealing their coins, and then the user may take some actions to
place the coins back into the vault before the relative timelock expires. There
seems to be no way to get this notification or observation period without a
vault construction. It might have been assumed it required a covenant.

Having a vault construction might go a long way to discourage would-be
attackers, on principle that the attacker might be incapable of recovering
their cost-of-attack because the recovery mechanism can lock up the coins
indefinitely. Griefing or denial-of-service would still be possible, of course,
but with multisig there might be some ways to put a halt to that as well. I am
working under the assumption that the attacker knows that the user is a vault
user.

Vaults
======

The idea is to have a sequence of pre-generated pre-signed transactions that
are generated in a certain way. The basic components are a vaulting transaction
that locks coins into a vault, a delayed-spend transaction which is the only
way to spend from a vault, and a re-vaulting transaction which can
recover/clawback coins from the delayed-spend transaction. The security of this
scheme is enforced by pre-signing transactions and deleting private keys, or
with the help of SIGHASH_NOINPUT then there's another scheme where private keys
are provably never known. This enforces that there's only a specific set of
possible outcomes at every step of the vault.

Some examples of what the set of broadcasted transactions might look like in
regular usage:

    coins -> VT -> DST -> exit via hot wallet key
    coins -> VT -> DST -> RVT
    coins -> VT -> DST -> RVT -> DST -> ...
    coins -> VT -> ... -> RVT998 -> nuclear abort

where:
    VT = vault transaction
    DST = delayed-spend transaction
    RVT = re-vaulting transaction

The delayed-spending transaction would have a single output with a script like:
(
    30 days AND hot wallet key
 OR 10 days AND re-vaulting public key
 OR 1 day AND 4-of-7 multisig
 OR 0 days and super-secure nuclear abort ragequit key
)

Another diagram:

    VT_100 -> DST -> (optionally) RVT -> coins are now in VT_99
    VT_99 -> DST -> (optionally) RVT -> coins are now in VT_98
    ...
    VT_1 -> burn-all-coins nuclear abort ragequit (final)

Definitions
===========

Transactions and components:

* Commitment/funding vault setup transaction. Signed after setting up the
transaction tree, and it is broadcasted whenever funds are to be placed into
the vault.

* Delayed-spend transaction. Signed during the vault transaction tree setup,
and it is broadcasted when the user wants to withdraw coins from cold storage
or otherwise manipulate the coins. The output script template used by the
delayed-spend transaction was defined earlier.

* Hot wallet key: Somewhat insecure key. This can also be multisig using
multiple hot keys.

* Re-vaulting key: It is important to note that the private key either never
existed (SIGHASH_NOINPUT + P2WPK for the re-vaulting transaction) or the
private key was deleted after pre-signing the re-vaulting transaction.

* 4-of-7 multisig: This is a group of differently-motivated individuals who are
responsible for signing transactions. This multisig group is not necessry to
describe the technique, I just think it's a useful feature for a vault to
include.

* Nuclear abort key: Also unnecessary. This is a key for which only a single
signed transaction will ever exist, and that single transaction will spend to a
proof-of-burn key like 0x00. This key must be extremely secure, and if there
is any doubt about the ability to keep such a key secured, then it is better to
not include this in the protocol. Alternatively, maybe include it as an option
50 layers down in the revaulting sequence.

* Nuclear-abort pre-signed transaction. This is signed during transaction tree
setup, before constructing the delayed-spend transaction. It is broadcasted
only if the user wants to provably relinquish coins forever without giving the
attacker any coins.

* Re-vaulting transaction. This is where the magic happens. The re-vaulting
transaction is signed during transaction tree setup, before constructing the
delayed-spend transaction for the parent vault. The re-vaulting transaction is
broadcasted when someone wants to prevent a coin withdrawal during the public
observation delay period. The re-vaulting transaction spends the delayed-spend
transaction outputs. It has a single output with a script created by running
the entire vault setup function again. Hence, when the re-vaulting transaction
is confirmed, all of the coins go back into a new identically-configured vault
instead of being relinquished through the delayed-spend transaction timeout for
hot wallet key signing.

* Special case: final transaction. This is the very first pre-signed
transaction during setup, and the transaction spends the coins using any
provable burn technique. This is broadcasted only at the end of the game, as an
ultimate abort and forfeiture of coins without giving in to an adversary. It's
similar to the nuclear-abort ragequit transaction but it sits at the same place
that a delayed-spend transaction would, at the very end of the rainbow or
yellow brick road.

Example log during vault setup
==============================

When running the recursive vault setup function, the created artifacts (in
order) will look like:

1) choose one of:
   (first iteration) pre-signed burn-all-coins nuclear abort ragequit (final)
   (all others) a new vault setup transaction spendable only by its
                delayed-spend transaction

2) pre-signed re-vaulting transaction sending to vault setup or final
transaction, with a unique private key

3) pre-signed delayed-spend transaction, with a unique private key

4) vault transaction spendable only by the delayed-spend public key

Pseudocode
==========

In pseudocode (where PTX is a pre-signed transaction function with
private key deletion):

    VT(counter, *args, **kwargs) =
        if counter == 0:
            DST = PTX("burn-all-coins")
        else:
            next_vault = VT(counter-1, *args, **kwargs)
            revaulting = PTX("only spendable by next_vault public key")
            DST = PTX("DST policy including revaulting and other conditions")
        vault = PTX("spendable only by this DST")
        return vault

Pre-signed transactions
=======================

What has been known for a while is that a covenant can be somewhat emulated
using a pre-signed transaction where the user then deletes the private key,
enforcing that the user's chosen policy must be enforced since there is only
one existing option and there will only ever be one option.

Such a scheme has been previously described for simple one-time and chained
vaults [3]. I have learned that the author has an implementation that is in
preparation, for a non-recursive version.

Note that a series of pre-signed transactions can be considered to be an
emulation of a covenant. Imagine a linear chain of pre-signed transactions
where each hop has a relative locktime before being able to broadcast the next
transaction. To recover the coins at the end of the rainbow, one would need to
broadcast each sequential transaction in order and wait for the relative
timelocks to expire each time. Here, covenants provide something like an undo
for bitcoin, but only between pre-determined addresses and scripts.

Fees for pre-signed transactions
================================

There's a few different techniques to talk about:

1) SIGHASH_SINGLE|SIGHASH_ANYONECANPAY to let someone add inputs and outputs.
This can get pretty complex though.

2) Add a zero-value OP_TRUE output and let anyone spend the zero-value output
and attach a child-pays-for-parent (CPFP) transaction to pay for everything.

3) Pre-sign a variety of different possible fee rates. Unfortunately this
involves an explosive blow-up in the amount of transaction data to generate. It
might actually be a reasonable blow-up amount, only resulting in a few hundred
megabytes of additional data. But given the other options, this is unnecessary.

Delete the key (for pre-signed transactions)
============================================

The delete-the-key trick is simple. The idea is to pre-sign at least one
transaction and then delete the private key, thus locking in that course of
action.

Unfortunately, delete-the-key doesn't really work for multisig scenarios
because nobody would trust that anyone else in the scheme has actually deleted
the secret. If they haven't deleted the secret, then they have full unilateral
control to sign anything in that branch of the transaction tree. The only time
that delete-the-key might be appropriate would be where the user who deletes
the key and controls the key during the setup process is also the sole
beneficiary of the entire setup with the multisig participants.

Alternative fee rates are easier to deal with using delete-the-key, compared to
a technique where the private key never existed which can only be used to sign
one fee rate per public key, requiring an entirely new vault subtree for each
alternative fee rate. With delete-the-key, the alternative fee rates are signed
with the private key before the private key is deleted.

Multisig gated by ECDSA pubkey recovery for provably-unknown keys
=================================================================

A group can participate in a multisig scheme with provably-unknown ECDSA keys.
Instead of deleting the key, the idea is to agree on a blockheight and then
select the blockhash (or some function of the chosen blockhash like
H(H(H(blockhash)))) as the signature. Next, the group agrees on a transaction
and they recover the public key from the signature using ECDSA pubkey recovery.
A pre-signed transaction is created, which will trigger the start of the public
observation period described earlier and also start the clock for the bip112
relative timelock on its output. In the output script, an OR branch
is added that enables the use of a re-vaulting key which could also be its own
separate multisig construction.

This is incompatible with P2WPKH because the P2WPKH spending scriptSig needs to
have the pubkey (to check the hash of the pubkey against the pubkeyhash in the
scriptPubKey), which in turn makes it incompatible with ECDSA pubkey recovery
which requires a hash of the message. However, with P2WPK and SIGHASH_NOINPUT
instead of P2WPKH it could conceivably work. SIGHASH_NOINPUT is required because
otherwise the input includes a txid which references the public key. With P2WPK,
the scriptSig only needs a signature and not a public key. Note that what would
be required is a version of SIGHASH_NOINPUT that does not commit to the public
key, and I think a few of the NOINPUT proposals are committing to the public
key.

Alternatively, there may be some constructions using the 2-party ECDSA
techniques or m-n party ECDSA techniques.

Deploying exceedingly large scripts
===================================

A brief interlude to share a somewhat obvious construction. I haven't seen this
written down yet.

Suppose there is a bitcoin script that someone is interested in using, but it
far exceeds the size limits and sigop limits. To fix this, they would split up
the script into usable chunks, and then use the delete-the-key mechanism (or
the other one) to create an OR branch that is signable by a single key for
which only a single signature is known. That new pre-signed transaction would
spend to a script that has the output with the remainder of the script of
interest. Re-vaulting or clawback clauses can be added to that output as well,
but spending back to the original root script will only work by generating new
scripts and keys (since the final hash isn't known until the whole tree is
constructed, it's a dependency loop).

Recursively-enforced multi-party multisig bitcoin vaults
========================================================

Ideally, to enforce a covenant with impossible fairy dust magic, we would ask
for a bitcoin transaction that could be self-referential because the
only-one-signature-ever trick requires that the signed message be known before
producing the signature, and the signature has to be known before the public
key can be known, and the public key would have to be included in the
self-referential message/transaction hash value. So, that's a dependency loop
and it doesn't work. It would be interesting to explore a variation of this
idea with masking, such that a value X can be replaced by a hash over the whole
script with the X value, even though the real script will have the hash.
Someone else can figure that one out for me :-).

Instead of the self-referential values attempting to reference the same
script that is in the process of being constructed, an alternative is to use
the same script template but populate it with different parameters. The script
template gets reused over and over again, all the way down the tree, until the
final transaction which could be >100 years into the future once done adding up
all the relative locktimes. In fact, to create and populate this terrifying
recursive script tree, the final transaction needs to be created first, and
then it is given as input to the script template function and that output is
then given to the script template function itself-- and so on. At each stage,
there are additional pre-signed transactions and values to remember.

This can be written as:

    final_transaction = TX(spend to 0x0000 to burn the coins)
    initial_transaction = F(F(...F(final_transaction))

    (This is missing parameters to indicate to the function what the spending
    keys requirements are to be.)

See earlier explanation for more details.

Each call to the template populating function produces values that each must be
preserved for a very long time. It is less safe to store all of the pre-signed
transactions together at the same time, but more convenient. With less
redundancy, there is an increased chance of losing data over time, which could
render the coins completely frozen. This doesn't particularly worry me because
forgetting a key has that property already, and this could be likened to
hundreds of megabytes of extra key data or something. Unlike the much smaller
covenant-based (opcode-based covenant) vault construction, the multiple layers
here can be separately stored and protected, which might be able to protect
against an adversary that has stolen some of the re-vaulting keys but not all
of them.

Optimizations can be made to store parameters for generating the remainder of
the tree, such as using deterministic key derivation, such that megabytes of
data wouldn't need to be long-term stored. Only the initial parameters would
need to be stored.

Financial privacy for custody
=============================

One of the concerns raised in [2] is that if all coins at an exchange are
stored together in the same vault, then attackers would be able to learn about
access control policies by observing scripts and keys. Some privacy can be
recovered by using segregated vaults, at the cost of additional setup
complexity and keeping more data in long-term storage.

However, note that I think vaults are also useful for personal cold storage
solutions.

Fail-deadly mechanism
=====================

An early nuclear abort option can be added to these scripts. This idea was
explored in [2]. This would be a very cold very secret key that would abort the
re-vaulting procedure and send all coins to a (provably) nonsense key. This
allows a vault user to destroy the coins instead of continuously monitoring the
bitcoin blockchain for the rest of his life. The attacker can't recover their
cost of attack if they never get the coins, and this eliminates an entire class
of potential attackers who are directly interested only in financial gain. The
disadvantage is that if the attacker finds the secret key for the fail-deadly
mechanism and uses it, then all of the coins are gone forever.

Multisig variations
===================

The re-vaulting key could be the same key at each layer, or only sometimes the
same key, or always a unique key stored separately in another secure location.

Additionally, these re-vaulting keys could be subjected to multisig schemes, as
well as Shamir secret sharing schemes or other secret sharing schemes.

The idea of adding the 4-of-7 multisig component is to avoid griefing
situations, at the cost of the additional security requirements for the 4-of-7
multisig group.

Key rotation for vaults
=======================

Keeping the same hot wallet key for 100 years is not advisable. Rotate the keys
by setting up a new vault construction and initiating a withdrawal transaction
from the old vault to the new vault.

Single-use seals
================

This proposal may have inadvertedly demonstrated a practical way to implement
Peter Todd's single-use seals concept [4]. I am hesitant to say so, though,
because I think he would ask for a more sophisticated way to verify seal
closure.

Paid defection
==============

It might be advisable to add small rewards for evidence of defection amongst
multiparty multisig setups. Besides amounts spendable by individual keys from a
multisig setup, it may be possible to use a zero-knowledge contingent payment
for a zero-knowledge statement like: I have a signature s over some message m
which validates for pubkey pk where pk is a member of the multisig group. Then
the zkcp transaction would pay for knowledge of defectors. The zkcp procedure
would require interaction with the defector, while the direct pubkey method
would not. This is similar to companies paying employees to quit when they
value the payment over the value of continued employment.

Handling change
===============

It is important to note that this vault setup is one-time and once-only. There
must only ever be one deposit into one vault. Also, spending some coins would
require sending the change amount back into a new vault.  Alternatively,
upfront work can be done to set a regular withdrawal stipend or assumption
about how many coins are left, such that the transaction tree can be
pre-generated for those possibilities, hence cutting down on future vault
reinitializations. It would also be possible to commit upfront to only ever
working in some minimum increment number of bitcoin or something.

It is very important to only fund the vault once, and only with the amount that
was configured when setting up the vault.

References
==========

[1] https://fc16.ifca.ai/bitcoin/papers/MES16.pdf

[2] http://www0.cs.ucl.ac.uk/staff/P.McCorry/preventing-cryptocurrency-exchange.pdf

[3] http://web.archive.org/web/20180503151920/https://blog.sldx.com/re-imagining-cold-storage-with-timelocks-1f293bfe421f?gi=da99a4a00f67

[4] https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2017-December/015350.html
or https://diyhpl.us/wiki/transcripts/building-on-bitcoin/2018/single-use-seals/
or https://petertodd.org/2016/closed-seal-sets-and-truth-lists-for-privacy

Acknowledgements
================

* Jeremy Rubin for pointing out something embarrassingly broken in an earlier
draft.

* Bob McElrath for telling me to use SIGHASH_NOINPUT which I proceeded to
promptly forget about.

* Andrew Poelstra for the OP_TRUE trick.

* Joe Rayhawk for paid defection.

* Tadge Dryja for pointing out a few differences between SIGHASH_NOINPUT
proposals.


Thank you,

- Bryan
http://heybryan.org/