Date: Tue, 29 Jun 2021 21:14:39 +0000
To: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
From: Andrew Chow <achow101-lists@achow101.com>
Reply-To: Andrew Chow <achow101-lists@achow101.com>
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Subject: [bitcoin-dev] BIP Proposals for Output Script Descriptors
Precedence: list

Hi All,

I've been working on formalizing the Output Script Descriptors that have
been available in Bitcoin Core for a while into BIPs. Since descriptors
are modular and have optional components, I've decided to split it into
7 BIPs, rather than a single one. The first describes descriptors in
general and does not specify any particular descriptor. However it does
describe the general operation, key expressions (including derivation
paths and key origin info), and the descriptor checksum. The following 6
BIPs specify the actual descriptors themselves. These are non-segwit
descriptor (pk, pkh, sh), segwit descriptors (wpkh, wsh), multisig
descriptors (multi, sortedmulti), the taproot descriptor (tr), the combo
descriptor, and opaque descriptors (raw, addr). This separation is so
that implementors can choose to not implement some descriptors and still
say which descriptors they support without being too difficult to
understand.

The text of all of the documents are below, and they can also be found
on github:https://github.com/achow101/bips/tree/descriptors/

Thanks,
Andrew Chow

---

<pre>
 =C2=A0 BIP: bip-descriptors-general
 =C2=A0 Layer: Applications
 =C2=A0 Title: Output Script Descriptors General Operation
 =C2=A0 Author: Pieter Wuille <pieter@wuille.net>
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Andrew Chow <andrew=
@achow101.com>
 =C2=A0 Comments-Summary: No comments yet.
 =C2=A0 Comments-URI:
https://github.com/bitcoin/bips/wiki/Comments:BIP-descriptors-general
 =C2=A0 Status: Draft
 =C2=A0 Type: Informational
 =C2=A0 Created: 2021-06-27
 =C2=A0 License: BSD-2-Clause
</pre>

=3D=3DAbstract=3D=3D

Output Script Descriptors are a simple language which can be used to
describe collections ofoutput scripts.
There can be many different descriptor fragments and functions.
This document describes the general syntax for descriptors, descriptor
checksums, and common expressions.

=3D=3DCopyright=3D=3D

This BIP is licensed under the BSD 2-clause license.

=3D=3DMotivation=3D=3D

Bitcoin wallets traditionally have stored a set of keys which are later
serialized and mutated to produce the output scripts that the wallet
watches and the addresses it provides to users.
Typically backups have consisted of solely the private keys, nowadays
primarily in the form of BIP 39 mnemonics.
However this backup solution is insuffient, especially since the
introduction of Segregated Witness which added new output types.
Given just the private keys, it is not possible for restored wallets to
know which kinds of output scripts and addresses to produce.
This has lead to incompatibilities between wallets when restoring a
backup or exporting data for a watch only wallet.

Further complicating matters are BIP 32 derivation paths.
Although BIPs 44, 49, and 84 have specified standard BIP 32 derivation
paths for different output scripts and addresses, not all wallets
support them nor use those derivation paths.
The lack of derivation path information in these backups and exports
leads to further incompatibilities between wallets.

Current solutions to these issues have not been generic and can be
viewed as being layer violations.
Solutions such as introducing different version bytes for extended key
serialization both are a layer violation (key derivation should be
separate from script type meaning) and specific only to a particular
derivation path and script type.

Output Script Descriptors introduces a generic solution to these issues.
Script types are specified explicitly through the use of Script Expressions=
.
Key derivation paths are specified explicitly in Key Expressions.
These allow for creating wallet backups and exports which specify the
exact scripts, subscripts (redeemScript, witnessScript, etc.), and keys
to produce.
With the general structure specified in this BIP, new Script Expressions
can be introduced as new script types are added.
Lastly, the use of common terminology and existing standards allow for
Output Script Descriptors to be engineer readable so that the results
can be understood at a glance.

=3D=3DSpecification=3D=3D

Descriptors consist of several types of expressions.
The top level expression is a <tt>SCRIPT</tt>.
This expression may be followed by <tt>#CHECKSUM</tt>, where
<tt>CHECKSUM</tt> is an 8 character alphanumeric descriptor checksum.

=3D=3D=3DScript Expressions=3D=3D=3D

Script Expressions (denoted <tt>SCRIPT</tt>) are expressions which
correspond directly with a Bitcoin script.
These expressions are written as functions and take arguments.
Such expressions have a script template which is filled with the
arguments correspondingly.
Expressions are written with a human readable identifier string with the
arguments enclosed with parentheses.
The identifier string should be alphanumeric and may include underscores.

The arguments to a script expression are defined by that expression itself.
They could be a script expression, a key expression, or some other
expression entirely.

=3D=3D=3DKey Expressions=3D=3D=3D

A common expression used as an argument to script expressions are key
expressions (denoted <tt>KEY</tt>).
These represent a public or private key and, optionally, information
about the origin of that key.
Key expressions can only be used as arguments to script expressions.

Key expressions consist of:
* Optionally, key origin information, consisting of:
** An open bracket <tt>[</tt>
** Exactly 8 hex characters for the fingerprint of the key where the
derivation starts (see BIP 32 for details)
** Followed by zero or more <tt>/NUM</tt> or <tt>/NUM'</tt>=C2=A0 path
elements to indicate the unhardened or hardened derivation steps between
the fingerprint and the key that follows.
** A closing bracket <tt>]</tt>
* Followed by the actual key, which is either:
** A hex encoded public key, which depending the script expression, may
be either:
*** 66 hex character string beginning with <tt>02</tt> or <tt>03</tt>
representing a compressed public key
*** 130 hex character string beginning with <tt>04</tt> representing an
uncompressed public key
*** 64 hex character string representing an x-only public key
** A [[https://en.bitcoin.it/wiki/Wallet_import_format|WIF]] encoded
private key
** <tt>xpub</tt> encoded extended public key or <tt>xprv</tt> encoded
extended private key (as defined in BIP 32)
*** Followed by zero or more <tt>/NUM</tt> or <tt>/NUM'</tt> path
elements indicating BIP 32 derivation steps to be taken after the given
extended key.
*** Optionally followed by a single <tt>/*</tt> or <tt>/*'</tt> final
step to denote all direct unhardened or hardened children.

If the <tt>KEY</tt> is a BIP 32 extended key, before output scripts can
be created, child keys must be derived using the derivation information
that follows the extended key.
When the final step is <tt>/*</tt> or <tt>/*'</tt>, an output script
will be produced for every child key index.
The derived key must be serialized as a compressed public key.

In the above specification, the hardened indicator <tt>'</tt> may be
replaced with alternative hardnened indicators of <tt>h</tt> or <tt>H</tt>.

=3D=3D=3DCharacter Set=3D=3D=3D

The expressions used in descriptors must only contain characters within
this character set so that the descriptor checksum will work.

The allowed characters are:
<pre>
0123456789()[],'/*abcdefgh@:$%{}
IJKLMNOPQRSTUVWXYZ&+-.;<=3D>?!^_|~
ijklmnopqrstuvwxyzABCDEFGH`#"\<space>
</pre>
Note that <tt><space></tt> on the last line is a space character.

This character set is written as 3 groups of 32 characters in this
specific order so that the checksum below can identify more errors.
The first group are the most common "unprotected" characters (i.e.
things such as hex and keypaths that do not already have their own
checksums).
Case errors cause an offset that is a multiple of 32 while as many
alphabetic characters are in the same group while following the previous
restrictions.

=3D=3D=3DChecksum=3D=3D=3D

Follwing the top level script expression is a single octothorpe
(<tt>#</tt>) followed by the 8 character checksum.
The checksum is an error correcting checksum similar to bech32.

The checksum has the following properties:
* Mistakes in a descriptor string are measured in "symbol errors". The
higher the number of symbol errors, the harder it is to detect:
** An error substituting a character from
<tt>0123456789()[],'/*abcdefgh@:$%{}</tt> for another in that set always
counts as 1 symbol error.
*** Note that hex encoded keys are covered by these characters. Extended
keys (<tt>xpub</tt> and <tt>xprv</tt>) use other characters too, but
also have their own checksum mechansim.
*** <tt>SCRIPT</tt> expression function names use other characters, but
mistakes in these would generally result in an unparsable descriptor.
** A case error always counts as 1 symbol error.
** Any other 1 character substitution error counts as 1 or 2 symbol errors.
* Any 1 symbol error is always detected.
* Any 2 or 3 symbol error in a descriptor of up to 49154 characters is
always detected.
* Any 4 symbol error in a descriptor of up to 507 characters is always
detected.
* Any 5 symbol error in a descriptor of up to 77 characters is always
detected.
* Is optimized to minimize the chance of a 5 symbol error in a
descriptor up to 387 characters is undetected
* Random errors have a chance of 1 in 2<super>40</super> of being
undetected.

The checksum itself uses the same character set as bech32:
<tt>qpzry9x8gf2tvdw0s3jn54khce6mua7l</tt>

Valid descriptor strings with a checksum must pass the criteria for
validity specified by the Python3 code snippet below.
The function <tt>descsum_check</tt> must return true when its argument
<tt>s</tt> is a descriptor consisting in the form <tt>SCRIPT#CHECKSUM</tt>.

<pre>
INPUT_CHARSET =3D
"0123456789()[],'/*abcdefgh@:$%{}IJKLMNOPQRSTUVWXYZ&+-.;<=3D>?!^_|~ijklmnop=
qrstuvwxyzABCDEFGH`#\"\\
"
CHECKSUM_CHARSET =3D "qpzry9x8gf2tvdw0s3jn54khce6mua7l"
GENERATOR =3D [0xf5dee51989, 0xa9fdca3312, 0x1bab10e32d, 0x3706b1677a,
0x644d626ffd]

def descsum_polymod(symbols):
 =C2=A0=C2=A0=C2=A0 """Internal function that computes the descriptor check=
sum."""
 =C2=A0=C2=A0=C2=A0 chk =3D 1
 =C2=A0=C2=A0=C2=A0 for value in symbols:
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 top =3D chk >> 35
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 chk =3D (chk & 0x7ffffffff) << =
5 ^ value
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 for i in range(5):
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 chk ^=
=3D GENERATOR[i] if ((top >> i) & 1) else 0
 =C2=A0=C2=A0=C2=A0 return chk

def descsum_expand(s):
 =C2=A0=C2=A0=C2=A0 """Internal function that does the character to symbol =
expansion"""
 =C2=A0=C2=A0=C2=A0 groups =3D []
 =C2=A0=C2=A0=C2=A0 symbols =3D []
 =C2=A0=C2=A0=C2=A0 for c in s:
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 if not c in INPUT_CHARSET:
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 return =
None
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 v =3D INPUT_CHARSET.find(c)
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 symbols.append(v & 31)
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 groups.append(v >> 5)
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 if len(groups) =3D=3D 3:
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 symbols=
.append(groups[0] * 9 + groups[1] * 3 + groups[2])
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 groups =
=3D []
 =C2=A0=C2=A0=C2=A0 if len(groups) =3D=3D 1:
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 symbols.append(groups[0])
 =C2=A0=C2=A0=C2=A0 elif len(groups) =3D=3D 2:
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 symbols.append(groups[0] * 3 + =
groups[1])
 =C2=A0=C2=A0=C2=A0 return symbols

def descsum_check(s):
 =C2=A0=C2=A0=C2=A0 """Verify that the checksum is correct in a descriptor"=
""
 =C2=A0=C2=A0=C2=A0 if s[-9] !=3D '#':
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 return False
 =C2=A0=C2=A0=C2=A0 if not all(x in CHECKSUM_CHARSET for x in s[-8:]):
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 return False
 =C2=A0=C2=A0=C2=A0 symbols =3D descsum_expand(s[:-9]) + [CHECKSUM_CHARSET.=
find(x) for x
in s[-8:]]
 =C2=A0=C2=A0=C2=A0 return descsum_polymod(symbols) =3D=3D 1
</pre>

This implements a BCH code that has the properties described above.
The entire descriptor string is first processed into an array of symbols.
The symbol for each character is its position within its group.
After every 3rd symbol, a 4th symbol is inserted which represents the
group numbers combined together.
This means that a change that only affects the position within a group,
or only a group number change, will only affect a single symbol.

To construct a valid checksum given a script expression, the code below
can be used:

<pre>
def descsum_create(s):
 =C2=A0=C2=A0=C2=A0 """Add a checksum to a descriptor without"""
 =C2=A0=C2=A0=C2=A0 symbols =3D descsum_expand(s) + [0, 0, 0, 0, 0, 0, 0, 0=
]
 =C2=A0=C2=A0=C2=A0 checksum =3D descsum_polymod(symbols) ^ 1
 =C2=A0=C2=A0=C2=A0 return s + '#' + ''.join(CHECKSUM_CHARSET[(checksum >> =
(5 * (7 -
i))) & 31] for i in range(8))

</pre>

=3D=3DBackwards Compatibility=3D=3D

Output script descriptors are an entirely new language which is not
compatible with any existing software.
However many components of the expressions reuse encodings and
serializations defined by previous BIPs.

Output script descriptors are designed for future extension with further
fragment types and new script expressions.
These will be specified in additional BIPs.

=3D=3DReference Implemntation=3D=3D

Descriptors have been implemented in Bitcoin Core since version 0.17.

---

<pre>
 =C2=A0 BIP: bip-descriptors-segwit
 =C2=A0 Layer: Applications
 =C2=A0 Title: segwit Output Script Descriptors
 =C2=A0 Author: Pieter Wuille <pieter@wuille.net>
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Andrew Chow <andrew=
@achow101.com>
 =C2=A0 Comments-Summary: No comments yet.
 =C2=A0 Comments-URI:
https://github.com/bitcoin/bips/wiki/Comments:BIP-descriptors-segwit
 =C2=A0 Status: Draft
 =C2=A0 Type: Informational
 =C2=A0 Created: 2021-06-27
 =C2=A0 License: BSD-2-Clause
</pre>

=3D=3DAbstract=3D=3D

This document specifies <tt>wpkh()</tt>, and <tt>wsh()</tt> output
script descriptors.
<tt>wpkh()</tt> descriptors take a key and produces a P2WPKH output script.
<tt>wsh()</tt> descriptors take a script and produces a P2WSH output script=
.

=3D=3DCopyright=3D=3D

This BIP is licensed under the BSD 2-clause license.

=3D=3DMotivation=3D=3D

Segregated Witness added 2 additional standard output script formats:
P2WPKH and P2WSH.
These expressions allow specifying those formats as a descriptor.

=3D=3DSpecification=3D=3D

Two new script expressions are defined: <tt>wpkh()</tt>, and <tt>wsh()</tt>=
.

=3D=3D=3D<tt>wpkh()</tt>=3D=3D=3D

The <tt>wpkh(KEY)</tt> expression can be used as a top level expression,
or inside of a <tt>sh()</tt> descriptor.
It takes a single key expression as an argument and produces a P2WPKH
output script.
Only keys which are/has compressed public keys can be contained in a
<tt>wpkh()</tt> expression.

The output script produced is:
<pre>
OP_0 <KEY_hash160>
</pre>

=3D=3D=3D<tt>wsh()</tt>=3D=3D=3D

The <tt>wsh(SCRIPT)</tt> expression can be used as a top level
expression, or inside of a <tt>sh()</tt> descriptor.
It takes a single script expression as an argument and produces a P2WSH
output script.
<tt>wsh()</tt> expressions also create a witnessScript which is required
in order to spend outputs which use its output script.
This redeemScript is the output script produced by the <tt>SCRIPT</tt>
argument to <tt>wsh()</tt>.
Any key expression found in any script expression contained by a
<tt>wsh()</tt> expression must only produce compresed public keys.

The output script produced is:
<pre>
OP_0 <SCRIPT_sha256>
</pre>

=3D=3DTest Vectors=3D=3D

TBD

=3D=3DBackwards Compatibility=3D=3D

<tt>wpkh()</tt>, and <tt>wsh()</tt> descriptors use the format and
general operation specified in
[[bip-descriptor-general.mediawiki|bip-descriptor-general]].
As these are a wholly new descriptors, they are not compatible with any
implementation.
However the scripts produced are standard scripts so existing software
are likely to be familiar with them.

=3D=3DReference Implemntation=3D=3D

<tt>wpkh()</tt>, and <tt>wsh()</tt> descriptors have been implemented in
Bitcoin Core since version 0.17.

---

<pre>
 =C2=A0 BIP: bip-descriptors-non-segwit
 =C2=A0 Layer: Applications
 =C2=A0 Title: Non-segwit Output Script Descriptors
 =C2=A0 Author: Pieter Wuille <pieter@wuille.net>
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Andrew Chow <andrew=
@achow101.com>
 =C2=A0 Comments-Summary: No comments yet.
 =C2=A0 Comments-URI:
https://github.com/bitcoin/bips/wiki/Comments:BIP-descriptors-non-segwit
 =C2=A0 Status: Draft
 =C2=A0 Type: Informational
 =C2=A0 Created: 2021-06-27
 =C2=A0 License: BSD-2-Clause
</pre>

=3D=3DAbstract=3D=3D

This document specifies <tt>pk()</tt>, <tt>pkh()</tt>, and <tt>sh()</tt>
output script descriptors.
<tt>pk()</tt> descriptors take a key and produces a P2PK output script.
<tt>pkh()</tt> descriptors take a key and produces a P2PKH output script.
<tt>sh()</tt> descriptors take a script and produces a P2SH output script.

=3D=3DCopyright=3D=3D

This BIP is licensed under the BSD 2-clause license.

=3D=3DMotivation=3D=3D

Prior to the activation of Segregated Witness, there were 3 main
standard output script formats: P2PK, P2PKH, and P2SH.
These expressions allow specifying those formats as a descriptor.

=3D=3DSpecification=3D=3D

Three new script expressions are defined: <tt>pk()</tt>, <tt>pkh()</tt>,
and <tt>sh()</tt>.

=3D=3D=3D<tt>pk()</tt>=3D=3D=3D

The <tt>pk(KEY)</tt> expression can be used in any context or level of a
descriptor.
It takes a single key expression as an argument and produces a P2PK
output script.
Depending on the higher level descriptors, there may be restrictions on
the type of public keys that can be included.
Such restrictions will be specified by those descriptors.

The output script produced is:
<pre>
<KEY> OP_CHECKSIG
</pre>

=3D=3D=3D<tt>pkh()</tt>=3D=3D=3D

The <tt>pkh(KEY)</tt> expression can be used as a top level expression,
or inside of either a <tt>sh()</tt> or <tt>wsh()</tt> descriptor.
It takes a single key expression as an argument and produces a P2PKH
output script.
Depending on the higher level descriptors, there may be restrictions on
the type of public keys that can be included.
Such restrictions will be specified by those descriptors.

The output script produced is:
<pre>
OP_DUP OP_HASH160 <KEY_hash160> OP_EQUALVERIFY OP_CHECKSIG
</pre>

=3D=3D=3D<tt>sh()</tt>=3D=3D=3D

The <tt>sh(SCRIPT)</tt> expression can only be used as a top level
expression.
It takes a single script expression as an argument and produces a P2SH
output script.
<tt>sh()</tt> expressions also create a redeemScript which is required
in order to spend outputs which use its output script.
This redeemScript is the output script produced by the <tt>SCRIPT</tt>
argument to <tt>sh()</tt>.

The output script produced is:
<pre>
OP_HASH160 <SCRIPT_hash160> OP_EQUAL
</pre>

=3D=3DTest Vectors=3D=3D

TBD

=3D=3DBackwards Compatibility=3D=3D

<tt>pk()</tt>, <tt>pkh()</tt>, and <tt>sh()</tt> descriptors use the
format and general operation specified in
[[bip-descriptor-general.mediawiki|bip-descriptor-general]].
As these are a wholly new descriptors, they are not compatible with any
implementation.
However the scripts produced are standard scripts so existing software
are likely to be familiar with them.

=3D=3DReference Implemntation=3D=3D

<tt>pk()</tt>, <tt>pkh()</tt>, and <tt>sh()</tt> descriptors have been
implemented in Bitcoin Core since version 0.17.

---

<pre>
 =C2=A0 BIP: bip-descriptors-tr
 =C2=A0 Layer: Applications
 =C2=A0 Title: tr() Output Script Descriptors
 =C2=A0 Author: Pieter Wuille <pieter@wuille.net>
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Andrew Chow <andrew=
@achow101.com>
 =C2=A0 Comments-Summary: No comments yet.
 =C2=A0 Comments-URI:
https://github.com/bitcoin/bips/wiki/Comments:BIP-descriptors-tr
 =C2=A0 Status: Draft
 =C2=A0 Type: Informational
 =C2=A0 Created: 2021-06-27
 =C2=A0 License: BSD-2-Clause
</pre>

=3D=3DAbstract=3D=3D

This document specifies <tt>tr()</tt> output script descriptors.
<tt>tr()</tt> descriptors take a key and optionally a tree of scripts
and produces a P2TR output script.

=3D=3DCopyright=3D=3D

This BIP is licensed under the BSD 2-clause license.

=3D=3DMotivation=3D=3D

Taproot added one additional standard output script format: P2TR.
These expressions allow specifying those formats as a descriptor.

=3D=3DSpecification=3D=3D

A new script expressions are defined: <tt>tr()</tt>.
A new expression is defined: Tree Expressions

=3D=3D=3DTree Expression=3D=3D=3D

A Tree Expression (denoted <tt>TREE</tt>) is an expression which
represents a tree of scripts.
The way the tree is represented in an output script is dependent on the
higher level expressions.

A Tree Expression is:
* Any Script Expression that is allowed at the level this Tree
Expression is in.
* A pair of Tree Expressions consisting of:
** An open brace <tt>{</tt>
** A Tree Expression
** A comma <tt>,</tt>
** A Tree Expression
** A closing brance <tt>}</tt>

=3D=3D=3D<tt>tr()</tt>=3D=3D=3D

The <tt>tr(KEY)</tt> or <tt>tr(KEY, TREE)</tt> expression can only be
used as a top level expression.
All key expressions under any <tt>tr()</tt> expression must create
x-only public keys.

<tt>tr(KEY</tt> takes a single key expression as an argument and
produces a P2TR output script which does not have a script path.
The keys produced by the key expression are used as the internal key as
specified by [[bip-0341.mediawiki#cite_ref-22-0|BIP 341]].
Specifically, "If the spending conditions do not require a script path,
the output key should commit to an unspendable script path instead of
having no script path.
This can be achieved by computing the output key point as ''Q =3D P +
int(hash<sub>TapTweak</sub>(bytes(P)))G''."

<pre>
internal_key:=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 lift_x(KEY)
32_byte_output_key: internal_key + int(HashTapTweak(bytes(internal_key)))G
scriptPubKey:=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 OP_1 <32_byte_output_key>
</pre>

<tt>tr(KEY, TREE)</tt> takes a key expression as the first argument, and
a tree expression as the second argument and produces a P2TR output
script which has a script path.
The keys produced by the first key expression are used as the internal
key as specified by
[[bip-0341.mediawiki#Constructing_and_spending_Taproot_outputs|BIP 341]].
The Tree expression becomes the Taproot script tree as described in BIP 341=
.
A merkle root is computed from this tree and combined with the internal
key to create the Taproot output key.

<pre>
internal_key:=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 lift_x(KEY)
merkle_root:=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 HashTapBranch(TREE)
32_byte_output_key: internal_key + int(HashTapTweak(bytes(internal_key)
|| merkle_root))G
scriptPubKey:=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 OP_1 <32_byte_output_key>
</pre>

=3D=3DTest Vectors=3D=3D

TBD

=3D=3DBackwards Compatibility=3D=3D

<tt>tr()</tt> descriptors use the format and general operation specified
in [[bip-descriptor-general.mediawiki|bip-descriptor-general]].
As these are a wholly new descriptors, they are not compatible with any
implementation.
However the scripts produced are standard scripts so existing software
are likely to be familiar with them.

Tree Expressions are largely incompatible with existing script
expressions due to the restrictions in those expressions.
As of 2021-06-27, the only allowed script expression that can be used in
a tree expression is <tt>pk()</tt>.
However there will be future BIPs that specify script expressions that
can be used in tree expressions.

=3D=3DReference Implemntation=3D=3D

<tt>tr()</tt> descriptors have been implemented in Bitcoin Core since
version 22.0.

---

<pre>
 =C2=A0 BIP: bip-descriptors-multi
 =C2=A0 Layer: Applications
 =C2=A0 Title: Multisig Output Script Descriptors
 =C2=A0 Author: Pieter Wuille <pieter@wuille.net>
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Andrew Chow <andrew=
@achow101.com>
 =C2=A0 Comments-Summary: No comments yet.
 =C2=A0 Comments-URI:
https://github.com/bitcoin/bips/wiki/Comments:BIP-descriptors-multi
 =C2=A0 Status: Draft
 =C2=A0 Type: Informational
 =C2=A0 Created: 2021-06-27
 =C2=A0 License: BSD-2-Clause
</pre>

=3D=3DAbstract=3D=3D

This document specifies <tt>multi()</tt>, and <tt>sortedmulti()</tt>
output script descriptors.
Both functions take a threshold and one or more public keys and produce
a multisig output script.
<tt>multi()</tt> specifies the public keys in the output script in the
order given in the descriptor while <tt>sortedmulti()</tt> sorts the
public keys lexicographically when the output script is produced.

=3D=3DCopyright=3D=3D

This BIP is licensed under the BSD 2-clause license.

=3D=3DMotivation=3D=3D

The most common complex script used in Bitcoin is a threshold multisig.
These expressions allow specifying multisig scripts as a descriptor.

=3D=3DSpecification=3D=3D

Two new script expressions are defined: <tt>multi()</tt>, and
<tt>sortedmulti()</tt>.
Both expressions produce the scripts of the same template and take the
same arguments.
They are written as <tt>multi(k,KEY_1,KEY_2,...,KEY_n)</tt>.
<tt>k</tt> is the threshold - the number of keys that must sign the
input for the script to be valid.
<tt>KEY_1,KEY_2,...,KEY_n</tt> are the key expressions for the multisig.
<tt>k</tt> must be less than or equal to <tt>n<tt>.

<tt>multi()</tt> and <tt>sortedmulti()</tt> expressions can be used as a
top level expression, or inside of either a <tt>sh()</tt> or
<tt>wsh()</tt> descriptor.
Depending on the higher level descriptors, there may be restrictions on
the type of public keys that can be included.

Depending on the higher level descriptors, there are also restrictions
on the number of keys that can be present, i.e. the maximum value of
<tt>n</tt>.
When used at the top level, there can only be at most 3 keys.
When used inside of a <tt>sh()</tt> expression, there can only be most
15 compressed public keys (this is limited by the P2SH script limit).
Otherwise the maximum number of keys is 20.

The output script produced also depends on the value of <tt>k</tt>. If
<tt>k</tt> is less than or equal to 16:
<pre>
OP_k KEY_1 KEY_2 ... KEY_n OP_CHECKMULTISIG
</pre>

if <tt>k</tt> is greater than 16:
<pre>
k KEY_1 KEY_2 ... KEY_n OP_CHECKMULTISIG
</pre>

=3D=3D=3D<tt>sortedmulti()</tt>=3D=3D=3D

The only change for <tt>sortedmulti()</tt> is that the keys are sorted
lexicographically prior to the creation of the output script.
This sorting is on the keys that are to be put into the output script,
i.e. after all extended keys are derived.

=3D=3D=3DMultiple Extended Keys</tt>=3D=3D=3D

When one or more the key expressions in a <tt>multi()</tt> or
<tt>sortedmulti()</tt> expression are extended keys, the derived keys
use the same child index.
This changes the keys in lockstep and allows for output scripts to be
indexed in the same way that the derived keys are indexed.

=3D=3DTest Vectors=3D=3D

TBD

=3D=3DBackwards Compatibility=3D=3D

<tt>multi()</tt>, and <tt>sortedmulti()</tt> descriptors use the format
and general operation specified in
[[bip-descriptor-general.mediawiki|bip-descriptor-general]].
As these are a wholly new descriptors, they are not compatible with any
implementation.
However the scripts produced are standard scripts so existing software
are likely to be familiar with them.

=3D=3DReference Implemntation=3D=3D

<tt>multi()</tt>, and <tt>multi()</tt> descriptors have been implemented
in Bitcoin Core since version 0.17.

---

<pre>
 =C2=A0 BIP: bip-descriptors-combo
 =C2=A0 Layer: Applications
 =C2=A0 Title: combo() Output Script Descriptors
 =C2=A0 Author: Pieter Wuille <pieter@wuille.net>
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Andrew Chow <andrew=
@achow101.com>
 =C2=A0 Comments-Summary: No comments yet.
 =C2=A0 Comments-URI:
https://github.com/bitcoin/bips/wiki/Comments:BIP-descriptors-combo
 =C2=A0 Status: Draft
 =C2=A0 Type: Informational
 =C2=A0 Created: 2021-06-27
 =C2=A0 License: BSD-2-Clause
</pre>

=3D=3DAbstract=3D=3D

This document specifies <tt>combo()</tt> output script descriptors.
These take a key and produce P2PK, P2PKH, P2WPKH, and P2SH-P2WPKH output
scripts if applicable to the key.

=3D=3DCopyright=3D=3D

This BIP is licensed under the BSD 2-clause license.

=3D=3DMotivation=3D=3D

In order to make the transition from traditional key based wallets to
descriptor based wallets easier, it is useful to be able to take a key
and produce the scripts which have traditionally been produced by wallet
software.

=3D=3DSpecification=3D=3D

A new top level script expression is defined: <tt>combo(KEY)</tt>.
This expression can only be used as a top level expression.
It takes a single key expression as an argument and produces either 2 or
4 output scripts, depending on the key.
A <tt>combo()</tt> expression always produces a P2PK and P2PKH script,
the same as putting the key in both a <tt>pk()</tt> and a <tt>pkh()</tt>
expression.
If the key is/has a compressed public key, then P2WPKH and P2SH-P2WPKH
scripts are also produced, the same as putting the key in both a
<tt>wpkh()</tt> and <tt>sh(wpkh())</tt> expression.

=3D=3DTest Vectors=3D=3D

TBD

=3D=3DBackwards Compatibility=3D=3D

<tt>combo()</tt> descriptors use the format and general operation
specified in [[bip-descriptor-general.mediawiki|bip-descriptor-general]].
As this is a wholly new descriptor, it is not compatible with any
implementation.
However the scripts produced are standard scripts so existing software
are likely to be familiar with them.

=3D=3DReference Implemntation=3D=3D

<tt>combo</tt> descriptors have been implemented in Bitcoin Core since
version 0.17.

---

<pre>
 =C2=A0 BIP: bip-descriptors-encap
 =C2=A0 Layer: Applications
 =C2=A0 Title: raw() and addr() Output Script Descriptors
 =C2=A0 Author: Andrew Chow <andrew@achow101.com>
 =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Pieter Wuille <piet=
er@wuille.net>
 =C2=A0 Comments-Summary: No comments yet.
 =C2=A0 Comments-URI:
https://github.com/bitcoin/bips/wiki/Comments:BIP-descriptors-raw
 =C2=A0 Status: Draft
 =C2=A0 Type: Informational
 =C2=A0 Created: 2021-06-27
 =C2=A0 License: BSD-2-Clause
</pre>

=3D=3DAbstract=3D=3D

This document specifies <tt>raw()</tt> and <tt>addr()</tt> output script
descriptors.
<tt>raw()</tt> encapsulates a raw script as a descriptor.
<tt>addr()</tt> encapsulates an address as a descriptor.

=3D=3DCopyright=3D=3D

This BIP is licensed under the BSD 2-clause license.

=3D=3DMotivation=3D=3D

In order to make descriptors maximally compatible with scripts in use
today, it is useful to be able to wrap any arbitrary output script or an
address into a descriptor.

=3D=3DSpecification=3D=3D

Two new script expressions are defined: <tt>raw()</tt> and <tt>addr()</tt>.

=3D=3D=3D<tt>raw()</tt>=3D=3D=3D

The <tt>raw(HEX)</tt> expression can only be used as a top level descriptor=
.
As the argument, it takes a hex string representing a Bitcoin script.
The output script produced by this descriptor is the script represented
by <tt>HEX</tt>.

=3D=3D=3D<tt>addr()</tt>=3D=3D=3D

The <tt>addr(ADDR)</tt> expression can only be used as a top level
descriptor.
It takes an address as its single argument.
The output script produced by this descriptor is the output script
produced by the address <tt>ADDR</tt>.

=3D=3DTest Vectors=3D=3D

TBD

=3D=3DBackwards Compatibility=3D=3D

<tt>raw()</tt> and <tt>addr()</tt> descriptors use the format and
general operation specified in
[[bip-descriptor-general.mediawiki|bip-descriptor-general]].
As this is a wholly new descriptor, it is not compatible with any
implementation.
The reuse of existing Bitcoin addresses allows for this to be more
easily implemented.

=3D=3DReference Implemntation=3D=3D

<tt>raw()</tt> and <tt>addr</tt> descriptors have been implemented in
Bitcoin Core since version 0.17.