<pre>
  BIP: 390
  Layer: Applications
  Title: musig() Descriptor Key Expression
  Author: Ava Chow <me@achow101.com>
  Comments-Summary: No comments yet.
  Comments-URI: https://github.com/bitcoin/bips/wiki/Comments:BIP-0390
  Status: Draft
  Type: Informational
  Created: 2024-06-04
  License: CC0-1.0
  Requires: 380
</pre>

==Abstract==

This document specifies a <tt>musig()</tt> key expression for output script descriptors.
<tt>musig()</tt> expressions take multiple keys and produce an aggregate public key using BIP 327.

==Copyright==

This BIP is licensed under the Creative Commons CC0 1.0 Universal license.

==Motivation==

BIP 327 introduces the MuSig2 Multi-Signature scheme. It is useful to have a way for keys to be used
in a MuSig2 aggregate key to be expressed in descriptors so that wallets can more easily use MuSig2.

==Specification==

A new key expression is defined: <tt>musig()</tt>.

===<tt>musig(KEY, KEY, ..., KEY)</tt>===

The <tt>musig(KEY, KEY, ..., KEY)</tt> expression can only be used inside of a <tt>tr()</tt>
expression as a key expression. It additionally cannot be nested within another <tt>musig()</tt>
expression. Participant public keys may be repeated. The aggregate public key is produced
by using the <tt>KeyAgg</tt> algorithm on all KEYs specified in the expression after performing all
specified derivation. As with script expressions, KEY can contain child derivation specified by
<tt>/*</tt>. A new aggregate public key will be computed for each child index. Keys must be sorted
with the <tt>KeySort</tt> algorithm after all derivation and prior to aggregation<ref>'''Why must
the keys be sorted prior to aggregation?''' Although the descriptor's written form sets an order
for the keys that could be used for aggregation, the order should not matter as MuSig2 philosophically
operates over a set of keys, with the order merely being an implementation detail in aggregation
itself. Requiring sorting of keys prior to aggregation enforces this philosophy as keys can be
written in the descriptor in any order with the end result still being the same. Furthermore, this
aids with recovery where the descriptor was not backed up as users will not need to also have
backed up, or guess, the correct order of keys.</ref>.

===<tt>musig(KEY, KEY, ..., KEY)/NUM/.../*</tt>===

<tt>musig(KEY, KEY, ..., KEY)/NUM/.../*</tt> expressions are also allowed, with the same usage
restrictions as in the previous section. The aggregate public key
is first computed as described above, with the keys also being sorted after all derivation and prior
to aggregation. Then further BIP 32 derivation will be performed on the aggregate public key as described in
[[bip-0328.mediawiki|BIP 328]]. As there is no aggregate private key,
only unhardened derivation from the aggregate public key is allowed, and thus the derivation steps
following the <tt>musig()</tt> expression cannot contain
<tt>/NUMh</tt> or <tt>/NUM'</tt> derivation steps nor <tt>/*h</tt>, or <tt>/*'</tt> child derivation.
For these <tt>musig()</tt> expressions, the KEY expressions contained within must be xpubs or derived from
xpubs, and cannot contain child derivation as specified by a <tt>/*</tt>, <tt>/*'</tt>, <tt>/*h</tt>, or multipath as specified with <tt>/<NUM;NUM;...></tt>.

==Test Vectors==

Valid descriptors containing followed by the scripts they produce. Descriptors involving derived child keys
will have the 0th, 1st, and 2nd scripts listed.

* <tt>rawtr(musig(KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYjgd9M7rFU74sHUHy8S,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66))</tt>
** <tt>5120789d937bade6673538f3e28d8368dda4d0512f94da44cf477a505716d26a1575</tt>
* <tt>tr(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66))</tt>
** <tt>512079e6c3e628c9bfbce91de6b7fb28e2aec7713d377cf260ab599dcbc40e542312</tt>
* <tt>rawtr(musig(xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL,xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y)/0/*)</tt>
** <tt>51209508c08832f3bb9d5e8baf8cb5cfa3669902e2f2da19acea63ff47b93faa9bfc</tt>
** <tt>51205ca1102663025a83dd9b5dbc214762c5a6309af00d48167d2d6483808525a298</tt>
** <tt>51207dbed1b89c338df6a1ae137f133a19cae6e03d481196ee6f1a5c7d1aeb56b166</tt>
* <tt>tr(musig(xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL,xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y)/0/*,pk(f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9))</tt>
** <tt>51201d377b637b5c73f670f5c8a96a2c0bb0d1a682a1fca6aba91fe673501a189782</tt>
** <tt>51208950c83b117a6c208d5205ffefcf75b187b32512eb7f0d8577db8d9102833036</tt>
** <tt>5120a49a477c61df73691b77fcd563a80a15ea67bb9c75470310ce5c0f25918db60d</tt>
* <tt>tr(f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,pk(musig(xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL,xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y)/0/*))</tt>
** <tt>512068983d461174afc90c26f3b2821d8a9ced9534586a756763b68371a404635cc8</tt>
** <tt>5120368e2d864115181bdc8bb5dc8684be8d0760d5c33315570d71a21afce4afd43e</tt>
** <tt>512097a1e6270b33ad85744677418bae5f59ea9136027223bc6e282c47c167b471d5</tt>
* <tt>tr(musig(xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL/1,xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL/1)/2)</tt>
** <tt>5120a17ceacd6422bd5ffd9f165807b254b7d68ad39f179cc4f11545a6835227e97c</tt>

Invalid descriptors

* <tt>musig()</tt> is not allowed in top-level <tt>pk()</tt>: <tt>pk(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66))</tt>
* <tt>musig()</tt> is not allowed in top-level <tt>pkh()</tt>: <tt>pkh(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66))</tt>
* <tt>musig()</tt> is not allowed in <tt>wpkh()</tt>: <tt>wpkh(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66))</tt>
* <tt>musig()</tt> is not allowed in <tt>combo()</tt>: <tt>combo(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66))</tt>
* <tt>musig()</tt> is not allowed in <tt>sh(wpkh())</tt>: <tt>sh(wpkh(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66)))</tt>
* <tt>musig()</tt> is not allowed in <tt>sh(wsh())</tt>: <tt>sh(wsh(pk(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66))))</tt>
* <tt>musig()</tt> is not allowed in <tt>wsh()</tt>: <tt>wsh(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66))</tt>
* <tt>musig()</tt> is not allowed in <tt>sh()</tt>: <tt>sh(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66))</tt>
* Ranged <tt>musig()</tt> requires all participants to be xpubs: <tt>tr(musig(02f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9,03dff1d77f2a671c5f36183726db2341be58feae1da2deced843240f7b502ba659,023590a94e768f8e1815c2f24b4d80a8e3149316c3518ce7b7ad338368d038ca66)/0/0)</tt>
* Cannot have ranged participants if <tt>musig()</tt> is also ranged: <tt>tr(musig(xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL/*,xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y)/0/*)</tt>
* Cannot have multipath participants if <tt>musig()</tt> is also multipath: <tt>tr(musig(xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL/<0;1>,xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y)/<2;3>)</tt>
* <tt>musig()</tt> cannot have hardened derivation steps: <tt>tr(musig(xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL,xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y)/0h/*)</tt>
* <tt>musig()</tt> cannot have hardened child derivation: <tt>tr(musig(xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL,xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y)/0/*h)</tt>

==Backwards Compatibility==

<tt>musig()</tt> expressions use the format and general operation specified in
[[bip-0380.mediawiki|BIP 380]]. As these are a set of wholly new expressions, they are not compatible
with any implementation. However the keys are produced using a standard process so existing software
are likely to be familiar with them.

==Rationale==

<references/>

==Reference Implementation==

The reference implementation is available in Bitcoin Core [[https://github.com/bitcoin/bitcoin/pull/31244|PR #31244]].

==Acknowledgements==

Thanks to Pieter Wuille, Andrew Poelstra, Sanket Kanjalkar, Salvatore Ingala, and all others who
participated in discussions on this topic.
