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Subject: [bitcoindev] OP_PAIRCOMMIT
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Hi All,

We propose to add a new opcode to tapscript, the newest member of the LNhance
opcode family, OP_PAIRCOMMIT.

LNhance is a package deal of CTV + CSFS + IKEY + PC specifically designed to
enable efficient rebindable channels, that can be grafted to a variety ofcovenant tree / channel factory constructions.

When evaluated, the `OP_PAIRCOMMIT` instruction:
* Pops the top two values off the stack,
* takes the "PairCommit" tagged SHA256 hash of the stack elements,
* pushes the resulting commitment on the top of the stack.

https://gist.github.com/moonsettler/d7f1fb88e3e54ee7ecb6d69ff126433b

PR: 1699 to https://github.com/bitcoin/bips

Q: Why not CAT?

A: OP_PAIRCOMMIT was specifically introduced so that we don't have a dependency
on CAT for efficient LN-Symmetry construction. If we already had CAT or had
reasonable assurances that CAT will be activated soon, the balance of tradeoffs
might have tipped against a late introduction of a new opcode to a concept that
was already floating out there.

Q: What is the difference between PAIRCOMMIT and CAT?

A: PAIRCOMMIT is domain separated from other implicit uses of hashing pieces of
data together. CAT allows for reconstructing and therefore inspecting sighashes
on the stack. And not only it allows for fine grained introspection, it also
allows for inspecting ancestor transactions. This makes CAT with the Poelstra
trick a way to implement state carrying covenants.
* If CAT has consensus, PAIRCOMMIT is an optimization of which we already have
plenty examples of in script
* If CAT has no consensus, PAIRCOMMIT gets the job done in regards to a veryspecific subset of behaviors, that explicitly do not include introspection.

BR.
moonsettler

--------------------------------------------------------------------------------

<pre>

BIP: ?

Layer: Consensus (soft fork)

Title: OP_PAIRCOMMIT

Author: moonsettler <

moonsettler@protonmail.com

>

Comments-Summary: No comments yet.

Comments-URI: <links to wiki page for comments>

Status: Draft

Type: Standards Track

Created: 2024-11-08

License: BSD-3-CLAUSE

</pre>

## Abstract

This BIP describes a new tapscript opcode `OP_PAIRCOMMIT` which

provide limited vector commitment functionality in tapscript.

When evaluated, the `OP_PAIRCOMMIT` instruction:

* Pops the top two values off the stack,

* takes the "PairCommit" tagged SHA256 hash of the stack elements,

* pushes the resulting commitment on the top of the stack.

## Motivation

To do LN-Symmetry contracts that don't require the nodes to keep old states,

we need to solve the data availability problem presented by unilateral closes.

Channel peers must be able to reconstruct the script that spends an

intermediate state.

Using in sequence `OP_CHECKTEMPLATEVERIFY`, `OP_PAIRCOMMIT`, `OP_INTERNALKEY`

and `OP_CHECKSIGFROMSTACK` we can construct a rebindable channel that is also

optimal.

If `OP_CAT` was available, it could be used to combine multiple stack elements,

that get verified with `OP_CHECKSIGFROMSTACK` as a valid state update.

`OP_PAIRCOMMIT` solves this specific problem without introducing a wide range

of potentially controversial new behaviors, such as novel 2-way peg mechanisms.

The number of SHA256 iterations is minimized in the primary use case we

can optimize for, which is LN-Symmetry. Since the Tag can be pre-computed as

mid-state, it would only take 1 or 2 hash cycles in validation for the

unilateral close scenario.

## Specification

Repurpose opcode 205 (currently `OP_SUCCESS`) as follows:

`OP_PAIRCOMMIT` pops two elements off the stack, then concatenates them along

with their size commitments and takes the tagged SHA256 hash of that

concatenated string, then pushes the resulting hash back on the stack.

Given the stack `[x1, x2]`, where `x2` is at the top of the stack:

`OP_PAIRCOMMIT` will push `SHA256(tagPC|cs(x1)|x1|cs(x2)|x2)` onto the stack.

Where `|` denotes concatenation and `tagPC` is calculated according to BIP-340

tagged hash as `SHA256("PairCommit")|SHA256("PairCommit")` and `cs(x)` means

`CompactSize(x)`.

### Implementation

```c++

case OP_PAIRCOMMIT: {

// OP_PAIRCOMMIT is only available in Tapscript

// ...

// x1 x2 -- hash

if (stack.size() < 2) {

return set_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);

}

const valtype& vch1 = stacktop(-2);

const valtype& vch2 = stacktop(-1);

uint256 hash = PairCommitHash(vch1, vch2);

popstack(stack);

popstack(stack);

stack.emplace_back(hash.begin(), hash.end());

break;

}

```

```c++

const HashWriter HASHER_PAIRCOMMIT{TaggedHash("PairCommit")};

uint256 PairCommitHash(const std::vector<unsigned char>& x1, const std::vector<unsigned char>& x2)

{

return (HashWriter{HASHER_PAIRCOMMIT} << x1 << x2).GetSHA256();

}

```

### Use in script

`OP_PAIRCOMMIT` can be used to commit to a vector of stack elements in a way

that is not vulnerable to various forms of witness malleability. It is however,

highly optimized for just 2 stack elements.

```text

# pc-hash = PC(a, PC(b, c))

<a> <b> <c> | PC PC <pc-hash> OP_EQUALVERIFY

```

### Use in LN-Symmetry

The following assembly-like pseudo-code shows a possible LN-Symmetry channel

construction, that provides data availability to spend to the latest state from

an earlier state pushed on-chain with a forced close by channel partner.

```text

# S = 500000000

# IK -> A+B

<sig> <state-n-recovery-data> <state-n-hash> | CTV PC IK CSFS <S+1> CLTV DROP

```

before funding sign first state template:

```text

# state-n-hash { nLockTime(S+n), out(contract, amount(A)+amount(B)) }

# settlement-n-hash { nSequence(2w), out(A, amount(A)), out(B, amount(B)) }

# state-n-recovery-data { settlement-n-hash or state-n-balance }

# contract for state n < m

IF

<sig> <state-m-recovery-data> <state-m-hash> | CTV PC IK CSFS <S+n+1> CLTV DROP

ELSE

<settlement-n-hash> CTV

ENDIF

```

## Reference Implementation

A reference implementation is provided here:

https://github.com/lnhance/bitcoin/pull/6/files

## Backward Compatibility

By constraining the behavior of OP_SUCCESS opcodes, deployment of the BIP

can be done in a backwards compatible, soft-fork manner. If anyone were to

rely on the OP_SUCCESS behavior of `OP_SUCCESS205`, `OP_PAIRCOMMIT` would

invalidate their spend.

## Deployment

TBD

## Credits

Jeremy Rubin, Brandon Black, Salvatore Ingala, Anthony Towns

## Copyright

This document is licensed under the 3-clause BSD license.

## References

1. LNhance bitcoin repository, [lnhance](

https://github.com/lnhance/bitcoin

)

2. LN-Symmetry, [eltoo](

https://github.com/instagibbs/bolts/blob/eltoo_draft/XX-eltoo-transactions.md

)

3. OP_CAT, [BIN-2024-0001](

https://github.com/bitcoin-inquisition/binana/blob/master/2024/BIN-2024-0001.md

)

4. OP_CHECKTEMPLATEVERIFY, [BIP-119](

https://github.com/bitcoin/bips/tree/master/bip-0119

)

5. OP_CHECKSIGFROMSTACK, [BIN-2024-0003](

https://github.com/bitcoin-inquisition/binana/blob/master/2024/BIN-2024-0003.md

)

6. OP_INTERNALKEY, [BIN-2024-0004](

https://github.com/bitcoin-inquisition/binana/blob/master/2024/BIN-2024-0004.md

)

7. Tagged hash, [BIP-340](

https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki

)

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--b1=_zaqQvmDDQHbTdw1KU4fVuG8d0QUJBATmaaN0eNsbl0
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<div style=3D"font-family: Arial, sans-serif; font-size: 14px;"><span style=
=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; f=
ont-weight: 400;"></span></div><span style=3D"font-family: Arial, sans-seri=
f; font-size: 14px; line-height: normal; font-weight: 400;">Hi All,</span><=
div><br></div><div><span style=3D"font-family: Arial, sans-serif; font-size=
: 14px; line-height: normal; font-weight: 400;">We propose to add a new opc=
ode to tapscript, the newest member of the LNhance</span></div><div><span s=
tyle=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: norma=
l; font-weight: 400;">opcode family, OP_PAIRCOMMIT.</span></div><div><br></=
div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; li=
ne-height: normal; font-weight: 400;">LNhance is a package deal of CTV + CS=
FS + IKEY + PC specifically designed to</span></div><div><span style=3D"fon=
t-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-wei=
ght: 400;">enable efficient rebindable channels, that can be grafted to a v=
ariety of</span></div><span style=3D"font-family: Arial, sans-serif; font-s=
ize: 14px; line-height: normal; font-weight: 400;">covenant tree / channel =
factory constructions.</span><div><br></div><div><span style=3D"font-family=
: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400=
;">When evaluated, the `OP_PAIRCOMMIT` instruction:</span></div><div><span =
style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: norm=
al; font-weight: 400;">* Pops the top two values off the stack,</span></div=
><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-=
height: normal; font-weight: 400;">* takes the "PairCommit" tagged SHA256 h=
ash of the stack elements,</span></div><div><span style=3D"font-family: Ari=
al, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">* =
pushes the resulting commitment on the top of the stack.</span></div><div><=
br></div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14p=
x; line-height: normal; font-weight: 400;"><a href=3D"https://gist.github.c=
om/moonsettler/d7f1fb88e3e54ee7ecb6d69ff126433b" title=3D"https://gist.gith=
ub.com/moonsettler/d7f1fb88e3e54ee7ecb6d69ff126433b">https://gist.github.co=
m/moonsettler/d7f1fb88e3e54ee7ecb6d69ff126433b</a></span></div><div><br></d=
iv><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; lin=
e-height: normal; font-weight: 400;">PR: 1699 to <a href=3D"https://github.=
com/bitcoin/bips" title=3D"https://github.com/bitcoin/bips">https://github.=
com/bitcoin/bips</a><br></span></div><div><br></div><span style=3D"font-fam=
ily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: =
400;">Q: Why not CAT?</span><div><br></div><div><span style=3D"font-family:=
 Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;=
">A: OP_PAIRCOMMIT was specifically introduced so that we don't have a depe=
ndency</span></div><div><span style=3D"font-family: Arial, sans-serif; font=
-size: 14px; line-height: normal; font-weight: 400;">on CAT for efficient L=
N-Symmetry construction. If we already had CAT or had</span></div><div><spa=
n style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: no=
rmal; font-weight: 400;">reasonable assurances that CAT will be activated s=
oon, the balance of tradeoffs</span></div><div><span style=3D"font-family: =
Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;"=
>might have tipped against a late introduction of a new opcode to a concept=
 that</span></div><div><span style=3D"font-family: Arial, sans-serif; font-=
size: 14px; line-height: normal; font-weight: 400;">was already floating ou=
t there.</span></div><div><br></div><div><span style=3D"font-family: Arial,=
 sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">Q: Wh=
at is the difference between PAIRCOMMIT and CAT?</span></div><div><br></div=
><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-=
height: normal; font-weight: 400;">A: PAIRCOMMIT is domain separated from o=
ther implicit uses of hashing pieces of</span></div><div><span style=3D"fon=
t-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-wei=
ght: 400;">data together. CAT allows for reconstructing and therefore inspe=
cting sighashes</span></div><div><span style=3D"font-family: Arial, sans-se=
rif; font-size: 14px; line-height: normal; font-weight: 400;">on the stack.=
 And not only it allows for fine grained introspection, it also</span></div=
><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-=
height: normal; font-weight: 400;">allows for inspecting ancestor transacti=
ons. This makes CAT with the Poelstra</span></div><div><span style=3D"font-=
family: Arial, sans-serif; font-size: 14px; line-height: normal; font-weigh=
t: 400;">trick a way to implement state carrying covenants.</span></div><di=
v><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-heig=
ht: normal; font-weight: 400;">* If CAT has consensus, PAIRCOMMIT is an opt=
imization of which we already have</span></div><div><span style=3D"font-fam=
ily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: =
400;">plenty examples of in script</span></div><div><span style=3D"font-fam=
ily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: =
400;">* If CAT has no consensus, PAIRCOMMIT gets the job done in regards to=
 a very</span></div><span style=3D"font-family: Arial, sans-serif; font-siz=
e: 14px; line-height: normal; font-weight: 400;">specific subset of behavio=
rs, that explicitly do not include introspection.</span><div style=3D""><di=
v></div><br></div><div style=3D""><span style=3D"font-family: Arial, sans-s=
erif; font-size: 14px; line-height: normal; font-weight: 400;">BR.</span></=
div><div style=3D""><span style=3D"font-family: Arial, sans-serif; font-siz=
e: 14px; line-height: normal; font-weight: 400;">moonsettler</span></div><d=
iv style=3D""><br></div><div style=3D""><span style=3D"font-family: Arial, =
sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">------=
--------------------------------------------------------------------------<=
/span><br></div><pre><span style=3D"font-family: Arial, sans-serif; font-si=
ze: 14px; line-height: normal; font-weight: 400;">&lt;pre&gt;</span><div><s=
pan style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: =
normal; font-weight: 400;">&nbsp; BIP: ?</span></div><div><span style=3D"fo=
nt-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-we=
ight: 400;">&nbsp; Layer: Consensus (soft fork)</span></div><div><span styl=
e=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; =
font-weight: 400;">&nbsp; Title: OP_PAIRCOMMIT</span></div><div><span style=
=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; f=
ont-weight: 400;">&nbsp; Author: moonsettler &lt;</span><span style=3D"font=
-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-weig=
ht: 400;">moonsettler@protonmail.com</span><span style=3D"font-family: Aria=
l, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">&gt=
;</span></div><div><span style=3D"font-family: Arial, sans-serif; font-size=
: 14px; line-height: normal; font-weight: 400;">&nbsp; Comments-Summary: No=
 comments yet.</span></div><div><span style=3D"font-family: Arial, sans-ser=
if; font-size: 14px; line-height: normal; font-weight: 400;">&nbsp; Comment=
s-URI: &lt;links to wiki page for comments&gt;</span></div><div><span style=
=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; f=
ont-weight: 400;">&nbsp; Status: Draft</span></div><div><span style=3D"font=
-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-weig=
ht: 400;">&nbsp; Type: Standards Track</span></div><div><span style=3D"font=
-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-weig=
ht: 400;">&nbsp; Created: 2024-11-08</span></div><div><span style=3D"font-f=
amily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight=
: 400;">&nbsp; License: BSD-3-CLAUSE</span></div><div><span style=3D"font-f=
amily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight=
: 400;">&lt;/pre&gt;</span></div><div><br></div><div><span style=3D"font-fa=
mily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight:=
 400;">## Abstract</span></div><div><br></div><div><span style=3D"font-fami=
ly: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 4=
00;">This BIP describes a new tapscript opcode `OP_PAIRCOMMIT` which</span>=
</div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; =
line-height: normal; font-weight: 400;">provide limited vector commitment f=
unctionality in tapscript.</span></div><div><br></div><div><span style=3D"f=
ont-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-w=
eight: 400;">When evaluated, the `OP_PAIRCOMMIT` instruction:</span></div><=
div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-he=
ight: normal; font-weight: 400;">* Pops the top two values off the stack,</=
span></div><div><span style=3D"font-family: Arial, sans-serif; font-size: 1=
4px; line-height: normal; font-weight: 400;">* takes the "PairCommit" tagge=
d SHA256 hash of the stack elements,</span></div><div><span style=3D"font-f=
amily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight=
: 400;">* pushes the resulting commitment on the top of the stack.</span></=
div><div><br></div><div><span style=3D"font-family: Arial, sans-serif; font=
-size: 14px; line-height: normal; font-weight: 400;">## Motivation</span></=
div><div><br></div><div><span style=3D"font-family: Arial, sans-serif; font=
-size: 14px; line-height: normal; font-weight: 400;">To do LN-Symmetry cont=
racts that don't require the nodes to keep old states,</span></div><div><sp=
an style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: n=
ormal; font-weight: 400;">we need to solve the data availability problem pr=
esented by unilateral closes.</span></div><div><span style=3D"font-family: =
Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;"=
>Channel peers must be able to reconstruct the script that spends an</span>=
</div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; =
line-height: normal; font-weight: 400;">intermediate state.</span></div><di=
v><br></div><div><span style=3D"font-family: Arial, sans-serif; font-size: =
14px; line-height: normal; font-weight: 400;">Using in sequence `OP_CHECKTE=
MPLATEVERIFY`, `OP_PAIRCOMMIT`, `OP_INTERNALKEY`</span></div><div><span sty=
le=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal;=
 font-weight: 400;">and `OP_CHECKSIGFROMSTACK` we can construct a rebindabl=
e channel that is also</span></div><div><span style=3D"font-family: Arial, =
sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">optima=
l.</span></div><div><br></div><div><span style=3D"font-family: Arial, sans-=
serif; font-size: 14px; line-height: normal; font-weight: 400;">If `OP_CAT`=
 was available, it could be used to combine multiple stack elements,</span>=
</div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; =
line-height: normal; font-weight: 400;">that get verified with `OP_CHECKSIG=
FROMSTACK` as a valid state update.</span></div><div><br></div><div><span s=
tyle=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: norma=
l; font-weight: 400;">`OP_PAIRCOMMIT` solves this specific problem without =
introducing a wide range</span></div><div><span style=3D"font-family: Arial=
, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">of p=
otentially controversial new behaviors, such as novel 2-way peg mechanisms.=
</span></div><div><br></div><div><span style=3D"font-family: Arial, sans-se=
rif; font-size: 14px; line-height: normal; font-weight: 400;">The number of=
 SHA256 iterations is minimized in the primary use case we</span></div><div=
><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-heigh=
t: normal; font-weight: 400;">can optimize for, which is LN-Symmetry. Since=
 the Tag can be pre-computed as</span></div><div><span style=3D"font-family=
: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400=
;">mid-state, it would only take 1 or 2 hash cycles in validation for the</=
span></div><div><span style=3D"font-family: Arial, sans-serif; font-size: 1=
4px; line-height: normal; font-weight: 400;">unilateral close scenario.</sp=
an></div><div><br></div><div><span style=3D"font-family: Arial, sans-serif;=
 font-size: 14px; line-height: normal; font-weight: 400;">## Specification<=
/span></div><div><br></div><div><span style=3D"font-family: Arial, sans-ser=
if; font-size: 14px; line-height: normal; font-weight: 400;">Repurpose opco=
de 205 (currently `OP_SUCCESS`) as follows:</span></div><div><br></div><div=
><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-heigh=
t: normal; font-weight: 400;">`OP_PAIRCOMMIT` pops two elements off the sta=
ck, then concatenates them along</span></div><div><span style=3D"font-famil=
y: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 40=
0;">with their size commitments and takes the tagged SHA256 hash of that</s=
pan></div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14=
px; line-height: normal; font-weight: 400;">concatenated string, then pushe=
s the resulting hash back on the stack.</span></div><div><br></div><div><sp=
an style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: n=
ormal; font-weight: 400;">Given the stack `[x1, x2]`, where `x2` is at the =
top of the stack:</span></div><div><br></div><div><span style=3D"font-famil=
y: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 40=
0;">`OP_PAIRCOMMIT` will push `SHA256(tagPC|cs(x1)|x1|cs(x2)|x2)` onto the =
stack.</span></div><div><br></div><div><span style=3D"font-family: Arial, s=
ans-serif; font-size: 14px; line-height: normal; font-weight: 400;">Where `=
|` denotes concatenation and `tagPC` is calculated according to BIP-340</sp=
an></div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14p=
x; line-height: normal; font-weight: 400;">tagged hash as `SHA256("PairComm=
it")|SHA256("PairCommit")` and `cs(x)` means</span></div><div><span style=
=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; f=
ont-weight: 400;">`CompactSize(x)`.</span></div><div><br></div><div><span s=
tyle=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: norma=
l; font-weight: 400;">### Implementation</span></div><div><br></div><div><s=
pan style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: =
normal; font-weight: 400;">```c++</span></div><div><span style=3D"font-fami=
ly: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 4=
00;">case OP_PAIRCOMMIT: {</span></div><div><span style=3D"font-family: Ari=
al, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">&n=
bsp; &nbsp; // OP_PAIRCOMMIT is only available in Tapscript</span></div><di=
v><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-heig=
ht: normal; font-weight: 400;">&nbsp; &nbsp; // ...</span></div><div><span =
style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: norm=
al; font-weight: 400;">&nbsp; &nbsp; // x1 x2 -- hash</span></div><div><spa=
n style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: no=
rmal; font-weight: 400;">&nbsp; &nbsp; if (stack.size() &lt; 2) {</span></d=
iv><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; lin=
e-height: normal; font-weight: 400;">&nbsp; &nbsp; &nbsp; &nbsp; return set=
_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);</span></div><div><span =
style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: norm=
al; font-weight: 400;">&nbsp; &nbsp; }</span></div><div><span style=3D"font=
-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-weig=
ht: 400;">&nbsp; &nbsp; const valtype&amp; vch1 =3D stacktop(-2);</span></d=
iv><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; lin=
e-height: normal; font-weight: 400;">&nbsp; &nbsp; const valtype&amp; vch2 =
=3D stacktop(-1);</span></div><div><br></div><div><span style=3D"font-famil=
y: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 40=
0;">&nbsp; &nbsp; uint256 hash =3D PairCommitHash(vch1, vch2);</span></div>=
<div><br></div><div><span style=3D"font-family: Arial, sans-serif; font-siz=
e: 14px; line-height: normal; font-weight: 400;">&nbsp; &nbsp; popstack(sta=
ck);</span></div><div><span style=3D"font-family: Arial, sans-serif; font-s=
ize: 14px; line-height: normal; font-weight: 400;">&nbsp; &nbsp; popstack(s=
tack);</span></div><div><span style=3D"font-family: Arial, sans-serif; font=
-size: 14px; line-height: normal; font-weight: 400;">&nbsp; &nbsp; stack.em=
place_back(hash.begin(), hash.end());</span></div><div><span style=3D"font-=
family: Arial, sans-serif; font-size: 14px; line-height: normal; font-weigh=
t: 400;">&nbsp; &nbsp; break;</span></div><div><span style=3D"font-family: =
Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;"=
>}</span></div><div><span style=3D"font-family: Arial, sans-serif; font-siz=
e: 14px; line-height: normal; font-weight: 400;">```</span></div><div><span=
 style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: nor=
mal; font-weight: 400;">```c++</span></div><div><span style=3D"font-family:=
 Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;=
">const HashWriter HASHER_PAIRCOMMIT{TaggedHash("PairCommit")};</span></div=
><div><br></div><div><span style=3D"font-family: Arial, sans-serif; font-si=
ze: 14px; line-height: normal; font-weight: 400;">uint256 PairCommitHash(co=
nst std::vector&lt;unsigned char&gt;&amp; x1, const std::vector&lt;unsigned=
 char&gt;&amp; x2)</span></div><div><span style=3D"font-family: Arial, sans=
-serif; font-size: 14px; line-height: normal; font-weight: 400;">{</span></=
div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; li=
ne-height: normal; font-weight: 400;">&nbsp; &nbsp; return (HashWriter{HASH=
ER_PAIRCOMMIT} &lt;&lt; x1 &lt;&lt; x2).GetSHA256();</span></div><div><span=
 style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: nor=
mal; font-weight: 400;">}</span></div><div><span style=3D"font-family: Aria=
l, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">```=
</span></div><div><span style=3D"font-family: Arial, sans-serif; font-size:=
 14px; line-height: normal; font-weight: 400;">### Use in script</span></di=
v><div><br></div><div><span style=3D"font-family: Arial, sans-serif; font-s=
ize: 14px; line-height: normal; font-weight: 400;">`OP_PAIRCOMMIT` can be u=
sed to commit to a vector of stack elements in a way</span></div><div><span=
 style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: nor=
mal; font-weight: 400;">that is not vulnerable to various forms of witness =
malleability. It is however,</span></div><div><span style=3D"font-family: A=
rial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">=
highly optimized for just 2 stack elements.</span></div><div><br></div><div=
><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-heigh=
t: normal; font-weight: 400;">```text</span></div><div><span style=3D"font-=
family: Arial, sans-serif; font-size: 14px; line-height: normal; font-weigh=
t: 400;"># pc-hash =3D PC(a, PC(b, c))</span></div><div><br></div><div><spa=
n style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: no=
rmal; font-weight: 400;">&lt;a&gt; &lt;b&gt; &lt;c&gt; | PC PC &lt;pc-hash&=
gt; OP_EQUALVERIFY</span></div><div><span style=3D"font-family: Arial, sans=
-serif; font-size: 14px; line-height: normal; font-weight: 400;">```</span>=
</div><div><br></div><div><span style=3D"font-family: Arial, sans-serif; fo=
nt-size: 14px; line-height: normal; font-weight: 400;">### Use in LN-Symmet=
ry</span></div><div><br></div><div><span style=3D"font-family: Arial, sans-=
serif; font-size: 14px; line-height: normal; font-weight: 400;">The followi=
ng assembly-like pseudo-code shows a possible LN-Symmetry channel</span></d=
iv><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; lin=
e-height: normal; font-weight: 400;">construction, that provides data avail=
ability to spend to the latest state from</span></div><div><span style=3D"f=
ont-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-w=
eight: 400;">an earlier state pushed on-chain with a forced close by channe=
l partner.</span></div><div><br></div><div><br></div><div><span style=3D"fo=
nt-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-we=
ight: 400;">```text</span></div><div><span style=3D"font-family: Arial, san=
s-serif; font-size: 14px; line-height: normal; font-weight: 400;"># S =3D 5=
00000000</span></div><div><span style=3D"font-family: Arial, sans-serif; fo=
nt-size: 14px; line-height: normal; font-weight: 400;"># IK -&gt; A+B</span=
></div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px;=
 line-height: normal; font-weight: 400;">&lt;sig&gt; &lt;state-n-recovery-d=
ata&gt; &lt;state-n-hash&gt; | CTV PC IK CSFS &lt;S+1&gt; CLTV DROP</span><=
/div><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; l=
ine-height: normal; font-weight: 400;">```</span></div><div><span style=3D"=
font-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-=
weight: 400;">before funding sign first state template:</span></div><div><s=
pan style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: =
normal; font-weight: 400;">```text</span></div><div><span style=3D"font-fam=
ily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: =
400;"># state-n-hash { nLockTime(S+n), out(contract, amount(A)+amount(B)) }=
</span></div><div><span style=3D"font-family: Arial, sans-serif; font-size:=
 14px; line-height: normal; font-weight: 400;"># settlement-n-hash { nSeque=
nce(2w), out(A, amount(A)), out(B, amount(B)) }</span></div><div><span styl=
e=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; =
font-weight: 400;"># state-n-recovery-data { settlement-n-hash or state-n-b=
alance }</span></div><div><br></div><div><span style=3D"font-family: Arial,=
 sans-serif; font-size: 14px; line-height: normal; font-weight: 400;"># con=
tract for state n &lt; m</span></div><div><span style=3D"font-family: Arial=
, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">IF</=
span></div><div><span style=3D"font-family: Arial, sans-serif; font-size: 1=
4px; line-height: normal; font-weight: 400;">&nbsp; &lt;sig&gt; &lt;state-m=
-recovery-data&gt; &lt;state-m-hash&gt; | CTV PC IK CSFS &lt;S+n+1&gt; CLTV=
 DROP</span></div><div><span style=3D"font-family: Arial, sans-serif; font-=
size: 14px; line-height: normal; font-weight: 400;">ELSE</span></div><div><=
span style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height:=
 normal; font-weight: 400;">&nbsp; &lt;settlement-n-hash&gt; CTV</span></di=
v><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line=
-height: normal; font-weight: 400;">ENDIF</span></div><div><span style=3D"f=
ont-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-w=
eight: 400;">```</span></div><div><br></div><div><span style=3D"font-family=
: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400=
;">## Reference Implementation</span></div><div><br></div><div><span style=
=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; f=
ont-weight: 400;">A reference implementation is provided here:</span></div>=
<div><br></div><div><span style=3D"font-family: Arial, sans-serif; font-siz=
e: 14px; line-height: normal; font-weight: 400;">https://github.com/lnhance=
/bitcoin/pull/6/files</span></div><div><br></div><div><span style=3D"font-f=
amily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight=
: 400;">## Backward Compatibility</span></div><div><br></div><div><span sty=
le=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal;=
 font-weight: 400;">By constraining the behavior of OP_SUCCESS opcodes, dep=
loyment of the BIP</span></div><div><span style=3D"font-family: Arial, sans=
-serif; font-size: 14px; line-height: normal; font-weight: 400;">can be don=
e in a backwards compatible, soft-fork manner. If anyone were to</span></di=
v><div><span style=3D"font-family: Arial, sans-serif; font-size: 14px; line=
-height: normal; font-weight: 400;">rely on the OP_SUCCESS behavior of `OP_=
SUCCESS205`, `OP_PAIRCOMMIT` would</span></div><div><span style=3D"font-fam=
ily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: =
400;">invalidate their spend.</span></div><div><br></div><div><span style=
=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; f=
ont-weight: 400;">## Deployment</span></div><div><br></div><div><span style=
=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; f=
ont-weight: 400;">TBD</span></div><div><br></div><div><span style=3D"font-f=
amily: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight=
: 400;">## Credits</span></div><div><br></div><div><span style=3D"font-fami=
ly: Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 4=
00;">Jeremy Rubin, Brandon Black, Salvatore Ingala, Anthony Towns</span></d=
iv><div><br></div><div><span style=3D"font-family: Arial, sans-serif; font-=
size: 14px; line-height: normal; font-weight: 400;">## Copyright</span></di=
v><div><br></div><div><span style=3D"font-family: Arial, sans-serif; font-s=
ize: 14px; line-height: normal; font-weight: 400;">This document is license=
d under the 3-clause BSD license.</span></div><div><br></div><div><span sty=
le=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal;=
 font-weight: 400;">## References</span></div><div><br></div><div><span sty=
le=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal;=
 font-weight: 400;">1. LNhance bitcoin repository, [lnhance](</span><span s=
tyle=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: norma=
l; font-weight: 400;">https://github.com/lnhance/bitcoin</span><span style=
=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; f=
ont-weight: 400;">)</span></div><div><span style=3D"font-family: Arial, san=
s-serif; font-size: 14px; line-height: normal; font-weight: 400;">2. LN-Sym=
metry, [eltoo](</span><span style=3D"font-family: Arial, sans-serif; font-s=
ize: 14px; line-height: normal; font-weight: 400;">https://github.com/insta=
gibbs/bolts/blob/eltoo_draft/XX-eltoo-transactions.md</span><span style=3D"=
font-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-=
weight: 400;">)</span></div><div><span style=3D"font-family: Arial, sans-se=
rif; font-size: 14px; line-height: normal; font-weight: 400;">3. OP_CAT, [B=
IN-2024-0001](</span><span style=3D"font-family: Arial, sans-serif; font-si=
ze: 14px; line-height: normal; font-weight: 400;">https://github.com/bitcoi=
n-inquisition/binana/blob/master/2024/BIN-2024-0001.md</span><span style=3D=
"font-family: Arial, sans-serif; font-size: 14px; line-height: normal; font=
-weight: 400;">)</span></div><div><span style=3D"font-family: Arial, sans-s=
erif; font-size: 14px; line-height: normal; font-weight: 400;">4. OP_CHECKT=
EMPLATEVERIFY, [BIP-119](</span><span style=3D"font-family: Arial, sans-ser=
if; font-size: 14px; line-height: normal; font-weight: 400;">https://github=
.com/bitcoin/bips/tree/master/bip-0119</span><span style=3D"font-family: Ar=
ial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;">)=
</span></div><div><span style=3D"font-family: Arial, sans-serif; font-size:=
 14px; line-height: normal; font-weight: 400;">5. OP_CHECKSIGFROMSTACK, [BI=
N-2024-0003](</span><span style=3D"font-family: Arial, sans-serif; font-siz=
e: 14px; line-height: normal; font-weight: 400;">https://github.com/bitcoin=
-inquisition/binana/blob/master/2024/BIN-2024-0003.md</span><span style=3D"=
font-family: Arial, sans-serif; font-size: 14px; line-height: normal; font-=
weight: 400;">)</span></div><div><span style=3D"font-family: Arial, sans-se=
rif; font-size: 14px; line-height: normal; font-weight: 400;">6. OP_INTERNA=
LKEY, [BIN-2024-0004](</span><span style=3D"font-family: Arial, sans-serif;=
 font-size: 14px; line-height: normal; font-weight: 400;">https://github.co=
m/bitcoin-inquisition/binana/blob/master/2024/BIN-2024-0004.md</span><span =
style=3D"font-family: Arial, sans-serif; font-size: 14px; line-height: norm=
al; font-weight: 400;">)</span></div><span style=3D"font-family: Arial, san=
s-serif; font-size: 14px; line-height: normal; font-weight: 400;">7. Tagged=
 hash, [BIP-340](</span><span style=3D"font-family: Arial, sans-serif; font=
-size: 14px; line-height: normal; font-weight: 400;">https://github.com/bit=
coin/bips/blob/master/bip-0340.mediawiki</span><span style=3D"font-family: =
Arial, sans-serif; font-size: 14px; line-height: normal; font-weight: 400;"=
>)</span></pre><div class=3D"protonmail_signature_block" style=3D"font-fami=
ly: Arial, sans-serif; font-size: 14px;"><div class=3D"protonmail_signature=
_block-proton"></div>
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