Hello list,

TL;DR: the core opcodes of MATT can build vaults with a very similar design
to OP_VAULT. Code example here:


In my previous emails about the MATT proposal for smart contracts in
bitcoin [1], I mostly focused on proving its generality; that is, it
allows arbitrary smart contracts thanks to fraud proofs.

While I still find this "completeness" result compelling, I spent more time
thinking about the framework itself; the construction is not very
if it turns simple things into complicated ones. Luckily, this is not the
In particular, in this email we will not merkleize anything (other than

This post describes some progress into formalizing the semantics of the core
opcodes, and demonstrates how they could be used to create vaults that seem
comparable to the ones built with OP_VAULT [2], despite using general

An implementation and some minimal tests matching the content of this
e-mail can be found in the link above, using the bitcoin-inquisition as the
base branch.

Note that the linked code is not well tested and is only intended for
exploratory and demonstrative purposes; therefore, bugs are likely at this

#    PART 1: MATT's core

In this section, I will discuss plausible semantics for the core opcodes
for MATT.

The two core opcodes are defined below as OP_CHECKINPUTCONTRACTVERIFY and

(the initial posts named them OP_CHECK{INPUT,OUTPUT}COVENANTVERIFY)

They enhance Script with the following capabilities:
  - decide the taptree of the output
  - embed some (dynamically computed) data in the output
  - access the embedded data in the current UTXO (if any)

The opcodes below are incomplete, as they only control the output's Script
not the amounts; more on that below.

Other than that, the semantics should be quite close to the "right" one for
the MATT framework.

### The opcodes

    // OP_CHECKINPUTCONTRACTVERIFY is only available in Tapscript
    if (sigversion == SigVersion::BASE || sigversion ==
SigVersion::WITNESS_V0) return set_error(serror, SCRIPT_ERR_BAD_OPCODE);
    // (x d -- )
    if (stack.size() < 2)
        return set_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);
    valtype& x = stacktop(-2);
    valtype& d = stacktop(-1);
    if (x.size() != 32 || d.size() != 32)
        return set_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);
    const XOnlyPubKey nakedXOnlyKey{Span<const unsigned char>{x.data(),
x.data() + 32}};
    const uint256 data(d);
    if (!execdata.m_internal_key.has_value())
        return set_error(serror, SCRIPT_ERR_UNKNOWN_ERROR);  // TODO
    // Verify that tweak(lift_x(x), d) equals the internal pubkey
    if (!execdata.m_internal_key.value().CheckDoubleTweak(nakedXOnlyKey,
&data, nullptr))
        return set_error(serror, SCRIPT_ERR_WRONGCONTRACTDATA);
    // OP_CHECKOUTPUTCONTRACTVERIFY is only available in Tapscript
    if (sigversion == SigVersion::BASE || sigversion ==
SigVersion::WITNESS_V0) return set_error(serror, SCRIPT_ERR_BAD_OPCODE);
    // (out_i x taptree d -- )
    if (stack.size() < 4)
        return set_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);
    int out_i = CScriptNum(stacktop(-4), fRequireMinimal).getint();
    valtype& x = stacktop(-3);
    valtype& taptree = stacktop(-2);
    valtype& d = stacktop(-1);
    auto outps = checker.GetTxvOut();
    // Return error if the evaluation context is unavailable
    if (!outps)
        return set_error(serror, SCRIPT_ERR_UNKNOWN_ERROR); // TODO
    if (x.size() != 32 || taptree.size() != 32 || (d.size() != 0 &&
d.size() != 32))
        return set_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);
    if (out_i < 0 || out_i >= (int)outps->size())
        return set_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);
    const XOnlyPubKey nakedXOnlyKey{Span<const unsigned char>{x.data(),
x.data() + 32}};
    const uint256 data(d);
    const uint256 *data_ptr = (d.size() == 0 ? nullptr : &data);
    const uint256 merkle_tree(taptree);
    CScript scriptPubKey = outps->at(out_i).scriptPubKey;
    if (scriptPubKey.size() != 1 + 1 + 32 || scriptPubKey[0] != OP_1 ||
scriptPubKey[1] != 32)
        return set_error(serror, SCRIPT_ERR_WRONGCONTRACTDATA);
    const XOnlyPubKey outputXOnlyKey{Span<const unsigned
char>{scriptPubKey.data() + 2, scriptPubKey.data() + 34}};
    // Verify that taptweak(tweak(lift_x(x), d), taptree) equals the
internal pubkey
    if (!outputXOnlyKey.CheckDoubleTweak(nakedXOnlyKey, data_ptr,
        return set_error(serror, SCRIPT_ERR_WRONGCONTRACTDATA);

### Commentary

CheckDoubleTweak function (implemented in the branch) gets an x-only pubkey,
optionally some data, and optionally taptree's merkle root.
It verifies that the x-only pubkey being tested equals the given naked
optionally tweaked with the embedded data, optionally tweaked with the
hash of the merkle tree per BIP-0341 [3].
Making both the tweaks optional allows to simplify the code, and also to
more compact scripts in some spending paths.

In words:

- OP_CHECKINPUTCONTRACTVERIFY: verify that the current input's internal key
  contains some embedded data (which would typically be passed through the
  witness stack)
- OP_CHECKOUTPUTCONTRACTVERIFY: verify that a given output is a certain P2TR
  output script containing the desired embedded data.

TBD if the tweaking used for the embedded data tweak should use a tagged
omitted for simplicity in this demo implementation.

### Amount preservation

In the code above and in the linked demo implementation, the opcodes only
operate on the scriptPubkey; a complete implementation would want to make
that amounts are correctly preserved.

The most direct and general way to address this would be to allow direct
introspection on the output amounts. This has the complication that output
amounts require 64-bits arithmetics, as discussed in the context of other
proposals, for example: [4].

One more limited approach that works well for many interesting contracts
is that of the deferred checks, implemented in OP_VAULT [2].
The idea is that all the amounts of the inputs that commit to the same
script with OP_CHECKOUTPUTCONTRACTVERIFY are added together, and the script
interpreter requires that the amount of that output is not smaller than the
total amount of those inputs. This check is therefore transaction-wide
than being tested during the input's script evaluation.

This behaviour is adequate for vaults and likely suitable for many other
applications; however, it's not the most general approach. I didn't try to
implement it yet, and defer the decision on the best approach to a later

### Extensions

The opcodes above are not enough for the full generality of MATT: one would
need to add an opcode like OP_SHA256CAT to allow the data embedding to
to multiple pieces of data.
This is not used in today's post, therefore I left it out of these code

It would be easy to extend OP_CHECKOUTPUTCONTRACTVERIFY to also apply for
an arbitrary input (typically, different from the currently executed one);
are likely use cases for that, allowing to define contracts with more
cross-input semantics, but I preferred to keep things simple.

Of course, one could also entirely replace CICV/COCV with generic full
introspection on inputs/output's program, plus opcodes for elliptic curve
and tagged hashes.

#    PART 2: Vaults with MATT

In the rest of this post, I will document the first attempt at creating a
using the opcodes described.

While not an attempt at cloning exactly the functionality of OP_VAULT [2],
it borrows heavily from the excellent work that was done there.

In particular, it also inherits the choice of using OP_CTV as a primitive,
building on top of the bitcoin-inquisition's current branch that has already
merged OP_CTV. Reasonable vaults would be possible without CTV, but they
would be less efficient, particularly in the case of sending to many
in a single unvaulting flow.

### Distilling OP_VAULT

Abstracting from the implementation details, I mentally model a vault as a
simple state machine with 2 states: [V] and [U]:

[V]: the initial vault UTXO(s);
[U]: the utxo produced by the "trigger transaction" during unvaulting.

On the typical path: one or more [V] UTXOs are sent to the [U] state, and
a timelock set on [U] expires, [U] is spent to one or several destinations.
Crucially, the destination outputs and amounts are already decided when [V]
spent into [U].

At any time before the funds are spent from [U], they can always be spent by
sending them to some specified recovery path.

There are two key elements that are part of OP_VAULT's semantics, and could

− Forcing the script/amount of the next stepon
− Storing some data for future Script's access (in the vault's case, a hash
   that commits to the final withdrawal transaction).

CICV/COCV generalize both to arbitrary scripts (taptrees) and state
and to dynamical and witness-dependent data embedded in the pubkey of a P2TR

### Vault parameters

A contract that represents a vault has the following parameters (hardcoded
the script when the vault is created):

- alternate_pk: a key that can be used any time.
- spend_delay: the relative timelock before the withdrawal can be finalized;
- recover_pk: a pubkey for a P2TR output where funds can be sent at any

The alternate_pk is a pubkey that can optionally be used as the key-path
spending condition for both states [V] and [U]. If such a spending
condition is not
desired, it can be replaced with a NUMS point, making the key-path

The spend_delay is the number of blocks that must be mined before the final
withdrawal transaction

In this example we also use an unvault_pk needed to authorize the unvaulting
process (that is, spend [V] into [U]); this could be replaced with any
or other conditions expressible in Script.

### P2TR structure for [V] (vault)

internal key: alternate_pk

Script 1: "trigger"
        # witness: <out_i> <ctv-hash>
    <merkle root of U's taptree>,
    2, OP_ROLL,


Script 2: "recover"
        # witness: <out_i>
    OP_0,                          # no data tweak
    OP_0,                          # no taptweak

The "trigger" script requires in the witness an output index and the
that describes the withdrawal transaction.
COCV forces the output to contain the ctv-hash as embedded data.
That's followed by the unvaulting condition − in this example, a simple
signature check.

The "recover" script doesn't require any signature, and it simply forces
the output specified in the witness to be a P2TR output with recover_pk as

(Omitting the "recover" script in [V] would reduce the size of the witness
32 bytes in the expected case, and might be preferred for some users)

### P2TR structure for [U] (unvaulting state)

internal key: alternate_pk (tweaked with ctv_hash)

Script 1: "withdrawal"
        # witness: <ctv_hash>

    # check that the top of the stack is the
    # embedded data in the current input
    <alternate_pk>, OP_SWAP,

    # Check timelock

    # Check that the transaction output is as expected

Script 2: "recover"
        # witness: <out_i>

The "withdrawal" finalizes the transaction, by checking that the timelock
expired and
the outputs satisfy the CTV hash that was committed to in the previous

The "recover" script is identical as before.

### Differences with OP_VAULT vaults

Here I refer to the latest version of OP_VAULT at the time of writing. [5]
It is not a thorough analysis.

Unlike the implementation based on OP_VAULT, the [V] utxos don't have an
to add an additional output that is sent back to the same exact vault.
Supporting this use case seems to require a more general way of handling the
distribution of amounts than what I discussed in the section above: that
in fact need to be generalized to the case of multiple
OP_CHECKOUTPUTCONTRACTVERIFY opcodes executed for the same input.

By separating the ctv-hash (which is considered "data") from the scripts in
taptree, one entirely avoids the need to dynamically create taptrees and
replace leaves in the covenant-encumbered UTXOs; in fact, the taptrees of
and [U] are already set in stone when [V] utxos are created, and only the
"data" portion of [U]'s scriptPubKey is dynamically computed. In my opinion,
this makes it substantially easier to program "state machines" that control
behavior of coins, of which vaults are a special case.

I hope you'll find this interesting, and look forward to your comments.

Salvatore Ingala

[1] -
[2] - https://github.com/bitcoin/bips/pull/1421
[3] - https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki
[4] -
[5] -
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