<pre>
  BIP: 390
  Layer: Applications
  Title: musig() Descriptor Key Expression
  Authors: Ava Chow <me@achow101.com>
  Status: Draft
  Type: Informational
  Assigned: 2024-06-04
  License: CC0-1.0
  Version: 0.2.0
  Requires: 380, 328
</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-0327.mediawiki|BIP-327]].

==Copyright==

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

==Motivation==

[[bip-0327.mediawiki|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>.

In the following sections, the term <tt>KEY</tt> refers to key expressions as defined in [[bip-0380.mediawiki|BIP-380]]
and [[bip-0389.mediawiki|BIP-389]].

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

The <tt>musig(KEY, KEY, ..., KEY)</tt> expression can only be used inside of a <tt>tr()</tt>, <tt>rawtr()</tt>
or <tt>sp()</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 if no KEY expression
contains child derivation as specified by <tt>/*</tt> or multipath as specified with
<tt>/<NUM;NUM;...></tt>, in addition to the same usage restrictions as in the previous section. The KEY expressions
additionally must be xpubs or derived from xpubs. 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-0032.mediawiki|BIP-32]] derivation will be performed on the aggregate public key as described in
[[bip-0328.mediawiki|BIP-328]]. The <tt>/NUM/.../*</tt> following the <tt>musig()</tt> specifies
the derivation path to be used when deriving from the aggregate public key. <tt>/*</tt> is also
optional. As there is no aggregate private key, only unhardened derivation from the aggregate public
key is allowed. Thus these derivation steps cannot contain <tt>/NUMh</tt> or <tt>/NUM'</tt>
nor can child derivation be specified as <tt>/*h</tt>, or <tt>/*'</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>
* <tt>musig()</tt> cannot have participants with child derivation when <tt>musig()</tt> has derivation steps: <tt>tr(musig(xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL/*,xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y/*)/1/2)</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]].

==Changelog==

* __0.2.0__ (2026-03-04) - Allow <tt>musig()</tt> inside <tt>sp()</tt> expressions.
* __0.1.0__ (2025-12-08) - Allow <tt>musig()</tt> inside <tt>rawtr()</tt> expressions.

==Acknowledgements==

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