Subject: [bitcoindev] Proposed BIP text for Miniscript

From: "'Ava Chow' via Bitcoin Development Mailing List" <[email-masked]>
Date: Thu, 16 May 2024 19:21:10 +0000

Hi All,

Although Miniscript has been implemented and is in use by a couple of 
implementations, it doesn't have a formal BIP. As such, I and a few 
others have adapted the reference website's documentation to be in the 
BIP format, which is provided below. The text, and any changes that may 
be made, is also available at 
https://github.com/achow101/bips/blob/miniscript/bip-miniscript.md.

Any feedback on this, particularly about what else should be included, 
or what could be excluded, would be welcome.

Thanks,
Ava

***

<pre>
   BIP: miniscript
   Layer: Applications
   Title: Miniscript
   Author: Pieter Wuille <[email-masked]>
           Andrew Poelstra <[email-masked]>
           Sanket Kanjalkar <[email-masked]>
           Antoine Poinsot <[email-masked]>
           Ava Chow <[email-masked]>
   Comments-Summary: No comments yet.
   Comments-URI: 
https://github.com/bitcoin/bips/wiki/Comments:BIP-miniscript
   Status: Draft
   Type: Informational
   Created: 2023-10-10
   License: CC0-1.0
</pre>

## Abstract

This document specifies Miniscript, a language for writing (a subset of) 
Bitcoin Scripts in a
structured way, enabling analysis, composition, generic signing and more.

## Copyright

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

## Motivation

Bitcoin Script is an unusual stack-based language with many edge cases, 
designed for implementing
spending conditions consisting of various combinations of signatures, 
hash locks, and time locks.
Yet despite being limited in functionality it is still highly nontrivial to:

* Given a combination of spending conditions, finding the most 
economical script to implement it.
* Given two scripts, construct a script that implements a composition of 
their spending conditions (e.g. a multisig where one of the "keys" is 
another multisig).
* Given a script, find out what spending conditions it permits.
* Given a script and access to a sufficient set of private keys, 
construct a general satisfying witness for it.
* Given a script, be able to predict the cost of spending an output.
* Given a script, know whether particular resource limitations like the 
ops limit might be hit when spending.

Miniscript functions as a representation for scripts that makes this 
sort of operations possible.
It has a structure that allows composition. It is very easy to 
statically analyze for various
properties (spending conditions, correctness, security properties, 
malleability, ...). It can be
targeted by spending policy compilers. Finally, compatible scripts can 
easily be converted to
Miniscript form - avoiding the need for additional metadata for e.g. 
signing devices that support
it.

## Specification

These specifications apply to P2WSH (BIP143) and Tapscript (BIP342) 
scripts, with only minor
variations between the two. Differences are noted inline. Unless 
explicitly stated specifications
apply to both.

### Translation Table

This table shows all Miniscript *fragments* and their associated 
semantics and Bitcoin Script.
Fragments that do not change the semantics of their subexpressions are 
called *wrappers*. Normal
fragments use a `fragment(arg1, arg2, ..)` notation, while wrappers are 
written using
prefixes separated from other fragments by a colon. The colon is dropped 
between subsequent
wrappers; e.g.  `dv:older(144)` is the `d:` wrapper applied to the
`v:` wrapper applied to the `older` fragment for 144 blocks.

The `pk`, `pkh`, and `and_n` fragments and `t:`,
`l:`, and `u:` wrappers are syntactic sugar for other Miniscripts, as listed
in the table below. Note that `<20>` are in hex representation in this 
document.

Miniscript fragments are expected to be used in [BIP 
382](bip-0382.mediawiki) `wsh()` descriptors
and [BIP 386](bip-0386.mediawiki) `tr()` descriptors. Key expressions 
are specified in
[BIP 380](bip-0380.mediawiki#user-content-Key_Expressions). 
Additionally, BIPs 382 and 386 specify
restrictions on key expressions and what they resolve to - these apply 
to key expressions in
Miniscript. BIP 382's key expression restrictions apply to Miniscript in 
P2WSH contexts, and BIP
386's key expression restrictions apply to Miniscript in P2TR contexts.

| Semantics                                                | Miniscript 
Fragment           | Bitcoin Script
|----------------------------------------------------------|-------------------------------|---------------
| false                                                    | 
`0`                           | `0`
| true                                                     | 
`1`                           | `1`
| check(key)                                               | 
`pk_k(key)`                   | `<key>`
|                                                          | 
`pk_h(key)`                   | ` DUP HASH160 <HASH160(key)> EQUALVERIFY `
|                                                          | `pk(key)` = 
`c:pk_k(key)`     | `<key> CHECKSIG`
|                                                          | `pkh(key)` 
= `c:pk_h(key)`    | ` DUP HASH160 <HASH160(key)> EQUALVERIFY CHECKSIG`
| nSequence ≥ n (and compatible)                           | 
`older(n)`                    | `<n> CHECKSEQUENCEVERIFY`
| nLockTime ≥ n (and compatible)                           | 
`after(n)`                    | `<n> CHECKLOCKTIMEVERIFY`
| len(x) = 32 and SHA256(x) = h                            | 
`sha256(h)`                   | `SIZE <20> EQUALVERIFY SHA256 <h> EQUAL`
| len(x) = 32 and HASH256(x) = h                           | 
`hash256(h)`                  | `SIZE <20> EQUALVERIFY HASH256 <h> EQUAL`
| len(x) = 32 and RIPEMD160(x) = h                         | 
`ripemd160(h)`                | `SIZE <20> EQUALVERIFY RIPEMD160 <h> EQUAL`
| len(x) = 32 and HASH160(x) = h                           | 
`hash160(h)`                  | `SIZE <20> EQUALVERIFY HASH160 <h> EQUAL`
| (X and Y) or Z                                           | 
`andor(X,Y,Z)`                | `[X] NOTIF [Z] ELSE [Y] ENDIF`
| X and Y                                                  | 
`and_v(X,Y)`                  | `[X] [Y]`
|                                                          | 
`and_b(X,Y)`                  | `[X] [Y] BOOLAND`
|                                                          | 
`and_n(X,Y)` = `andor(X,Y,0)` | `[X] NOTIF 0 ELSE [Y] ENDIF`
| X or Z                                                   | 
`or_b(X,Z)`                   | `[X] [Z] BOOLOR`
|                                                          | 
`or_c(X,Z)`                   | `[X] NOTIF [Z] ENDIF`
|                                                          | 
`or_d(X,Z)`                   | `[X] IFDUP NOTIF [Z] ENDIF`
|                                                          | 
`or_i(X,Z)`                   | `IF [X] ELSE [Z] ENDIF`
| X_1 + ... + X_n = k                                      | 
`thresh(k,X_1,...,X_n)`       | `[X_1] [X_2] ADD ... [X_n] ADD ... <k> 
EQUAL`
| check(key_1) + ... + check(key_n) = k *(P2WSH only)*     | 
`multi(k,key_1,...,key_n)`    | `<k> <key_1> ... <key_n> <n> CHECKMULTISIG`
| check(key_1) + ... + check(key_n) = k *(Tapscript only)* | 
`multi_a(k,key_1,...,key_n)`  | `<key_1> CHECKSIG <key_2> CHECKSIGADD 
... <key_n> CHECKSIGADD <k> NUMEQUAL`
| X (identities)                                           | 
`a:X`                         | `TOALTSTACK [X] FROMALTSTACK`
|                                                          | 
`s:X`                         | `SWAP [X]`
|                                                          | 
`c:X`                         | `[X] CHECKSIG`
|                                                          | `t:X` = 
`and_v(X,1)`          | `[X] 1`
|                                                          | 
`d:X`                         | `DUP IF [X] ENDIF`
|                                                          | 
`v:X`                         | `[X] VERIFY (or VERIFY version of last 
opcode in [X])`
|                                                          | 
`j:X`                         | `SIZE 0NOTEQUAL IF [X] ENDIF`
|                                                          | 
`n:X`                         | `[X] 0NOTEQUAL`
|                                                          | `l:X` = 
`or_i(0,X)`           | `IF 0 ELSE [X] ENDIF`
|                                                          | `u:X` = 
`or_i(X,0)`           | `IF [X] ELSE 0 ENDIF`

### Type System

Not every Miniscript expression can be composed with every other. Some 
return their result by
putting true or false on the stack; others can only abort or continue. 
Some require subexpressions
that consume an exactly known number of arguments, while others need a 
subexpression that has a
nonzero top stack element to satisfy. To model all these properties, we 
define a correctness type
system for Miniscript.

#### Correctness

Every miniscript expression has one of four basic types: "**B**" (base), 
"**V**" (verify),
"**K**" (key) and "**W**" (wrapped). Then there are 6 type modifiers 
which guarantee additional
properties: "**z**" (zero arg), "**o**" (one-arg), "**n**" (nonzero), 
"**d**"
(dissatisfiable), "**u**" (unit) and "**k**" (no timelock mixing).

The following table lists the correctness requirements for each of the 
Miniscript expressions, and
its type properties in function of those of their subexpressions.

| Miniscript                   | 
Requires                                              | Type | Properties
|------------------------------|-------------------------------------------------------|-------------|-----------
| `0` |                                                       | 
B           | z; u; d
| `1` |                                                       | 
B           | z; u
| `pk_k(key)` |                                                       | 
K           | o; n; d; u
| `pk_h(key)` |                                                       | 
K           | n; d; u
| `older(n)`, `after(n)`       | 1 &le; n &lt; 
2<sup>31</sup>                          | B           | z
| `sha256(h)` |                                                       | 
B           | o; n; d; u
| `ripemd160(h)` |                                                       
| B           | o; n; d; u
| `hash256(h)` |                                                       | 
B           | o; n; d; u
| `hash160(h)` |                                                       | 
B           | o; n; d; u
| `andor(X,Y,Z)`               | X is Bdu; Y and Z are both B, K, or 
V                 | same as Y/Z | 
z=z<sub>X</sub>z<sub>Y</sub>z<sub>Z</sub>; 
o=z<sub>X</sub>o<sub>Y</sub>o<sub>Z</sub> or 
o<sub>X</sub>z<sub>Y</sub>z<sub>Z</sub>; u=u<sub>Y</sub>u<sub>Z</sub>; 
d=d<sub>Z</sub>
| `and_v(X,Y)`                 | X is V; Y is B, K, or 
V                               | same as Y   | 
z=z<sub>X</sub>z<sub>Y</sub>; o=z<sub>X</sub>o<sub>Y</sub> or 
z<sub>Y</sub>o<sub>X</sub>; n=n<sub>X</sub> or 
z<sub>X</sub>n<sub>Y</sub>; u=u<sub>Y</sub>
| `and_b(X,Y)`                 | X is B; Y is 
W                                        | B           | 
z=z<sub>X</sub>z<sub>Y</sub>; o=z<sub>X</sub>o<sub>Y</sub> or 
z<sub>Y</sub>o<sub>X</sub>; n=n<sub>X</sub> or 
z<sub>X</sub>n<sub>Y</sub>; d=d<sub>X</sub>d<sub>Y</sub>; u
| `or_b(X,Z)`                  | X is Bd; Z is 
Wd                                      | B           | 
z=z<sub>X</sub>z<sub>Z</sub>; o=z<sub>X</sub>o<sub>Z</sub> or 
z<sub>Z</sub>o<sub>X</sub>; d; u
| `or_c(X,Z)`                  | X is Bdu; Z is 
V                                      | V           | 
z=z<sub>X</sub>z<sub>Z</sub>; o=o<sub>X</sub>z<sub>Z</sub>
| `or_d(X,Z)`                  | X is Bdu; Z is 
B                                      | B           | 
z=z<sub>X</sub>z<sub>Z</sub>; o=o<sub>X</sub>z<sub>Z</sub>; 
d=d<sub>Z</sub>; u=u<sub>Z</sub>
| `or_i(X,Z)`                  | both are B, K, or 
V                                   | same as X/Z | 
o=z<sub>X</sub>z<sub>Z</sub>; u=u<sub>X</sub>u<sub>Z</sub>; 
d=d<sub>X</sub> or d<sub>Z</sub>
| `thresh(k,X_1,...,X_n)`      | 1 &le; k &le; n; X<sub>1</sub> is Bdu; 
others are Wdu | B           | z=all are z; o=all are z except one is o; 
d; u
| `multi(k,key_1,...,key_n)`   | 1 &le; k &le; 
n                                       | B           | n; d; u
| `multi_a(k,key_1,...,key_n)` | 1 &le; k &le; 
n                                       | B           | d; u
| `a:X`                        | X is 
B                                                | W           | 
d=d<sub>X</sub>; u=u<sub>X</sub>
| `s:X`                        | X is 
Bo                                               | W           | 
d=d<sub>X</sub>; u=u<sub>X</sub>
| `c:X`                        | X is 
K                                                | B           | 
o=o<sub>X</sub>; n=n<sub>X</sub>; d=d<sub>X</sub>; u
| `d:X`                        | X is 
Vz                                               | B           | o; n; 
d; *(Tapscript only)* u
| `v:X`                        | X is 
B                                                | V           | 
z=z<sub>X</sub>; o=o<sub>X</sub>; n=n<sub>X</sub>
| `j:X`                        | X is 
Bn                                               | B           | 
o=o<sub>X</sub>; n; d; u=u<sub>X</sub>
| `n:X`                        | X is 
B                                                | B           | 
z=z<sub>X</sub>; o=o<sub>X</sub>; n=n<sub>X</sub>; d=d<sub>X</sub>; u

#### Malleability

Malleability is the ability for a third party (*not* a participant in 
the script) to modify an
existing satisfaction into another valid satisfaction. To analyze the 
malleability guarantees of a
script we define three additional type properties: "**s**" (signed), 
"**f**" (forced) and
"**e**" (expressive).

The following table lists the malleability properties and requirement of 
each fragment.

| Miniscript                   | Requires | Properties
|------------------------------|---------------------------------------------------------------------|-----------
| `0` | | s, e
| `1` | | f
| `pk_k(key)` | | s, e
| `pk_h(key)` | | s, e
| `older(n)` | | f
| `after(n)` | | f
| `sha256(h)` | |
| `ripemd160(h)` | |
| `hash256(h)` | |
| `hash160(h)` | |
| `andor(X,Y,Z)`               | e<sub>X</sub> and (s<sub>X</sub> or 
s<sub>Y</sub> or s<sub>Z</sub>) | s=s<sub>Z</sub> and (s<sub>X</sub> or 
s<sub>Y</sub>); f=f<sub>Z</sub> and (s<sub>X</sub> or f<sub>Y</sub>); 
e=e<sub>Z</sub> and (s<sub>X</sub> or f<sub>Y</sub>)
| `and_v(X,Y)` | | s=s<sub>X</sub> or s<sub>Y</sub>; f=s<sub>X</sub> or 
f<sub>Y</sub>
| `and_b(X,Y)` | | s=s<sub>X </sub>or s<sub>Y;</sub> 
f=f<sub>Xf</sub><sub>Y</sub> or s<sub>X</sub>f<sub>X</sub> or 
s<sub>Y</sub>f<sub>Y</sub>; 
e=e<sub>X</sub>e<sub>Y</sub>s<sub>X</sub>s<sub>Y</sub>
| `or_b(X,Z)`                  | e<sub>Xe</sub><sub>Z </sub>and 
(s<sub>X</sub> or s<sub>Z</sub>)     | s=s<sub>X</sub>s<sub>Z</sub>; e
| `or_c(X,Z)`                  | e<sub>X</sub> and (s<sub>X</sub> or 
s<sub>Z</sub>)                  | s=s<sub>X</sub>s<sub>Z</sub>; f
| `or_d(X,Z)`                  | e<sub>X</sub> and (s<sub>X</sub> or 
s<sub>Z</sub>)                  | s=s<sub>X</sub>s<sub>Z</sub>; 
f=f<sub>Z</sub>; e=e<sub>Z</sub>
| `or_i(X,Z)`                  | s<sub>X</sub> or 
s<sub>Z</sub>                                      | 
s=s<sub>X</sub>s<sub>Z</sub>; f=f<sub>X</sub>f<sub>Z</sub>; 
e=e<sub>X</sub>f<sub>Z</sub> or e<sub>Z</sub>f<sub>X</sub>
| `thresh(k,X_1,...,X_n)`      | all are e; at most k are 
non-s                                      | s=at most k-1 are non-s; 
e=all are s
| `multi(k,key_1,...,key_n)` | | s; e
| `multi_a(k,key_1,...,key_n)` | | s; e
| `a:X` | | s=s<sub>X</sub>; f=f<sub>X</sub>; e=e<sub>X</sub>
| `s:X` | | s=s<sub>X</sub>; f=f<sub>X</sub>; e=e<sub>X</sub>
| `c:X` | | s; f=f<sub>X</sub>; e=e<sub>X</sub>
| `d:X` | | s=s<sub>X</sub>; e
| `v:X` | | s=s<sub>X</sub>; f
| `j:X` | | s=s<sub>X</sub>; e=f<sub>X
| `n:X` | | s=s<sub>X</sub>; f=f<sub>X</sub>; e=e<sub>X</sub>

### Satisfaction

The following table shows all valid satisfactions and dissatisfactions 
for every Miniscript, using
satisfactions and dissatisfactions of its subexpressions. Multiple 
possibilities are separated by
semicolons. Some options are not actually necessary to produce correct 
witnesses, and are called
*non-canonical* options. They are listed for completeness, but 
~~[struckthrough]~~. The
fragments where a satisfaction or dissatisfaction does not exist will 
contain *(none)*. The
fragments where the satisfaction or dissatisfaction is to provide no 
data will contain *(empty)*.

| Miniscript                   | Dissatisfactions 
(dsat)                                 | Satisfactions (sat)
|------------------------------|---------------------------------------------------------|--------------------
| `0`                          | 
*(empty)*                                               | *(none)*
| `1`                          | 
*(none)*                                                | *(empty)*
| `pk_k(key)`                  | 
0                                                       | sig
| `pk_h(key)`                  | 0 
key                                                   | sig key
| `older(n)`                   | 
*(none)*                                                | *(empty)*
| `after(n)`                   | 
*(none)*                                                | *(empty)*
| `sha256(h)`                  | any 32-byte vector except the 
preimage                  | preimage
| `ripemd160(h)`               | any 32-byte vector except the 
preimage                  | preimage
| `hash256(h)`                 | any 32-byte vector except the 
preimage                  | preimage
| `hash160(h)`                 | any 32-byte vector except the 
preimage                  | preimage
| `andor(X,Y,Z)`               | dsat(Z) dsat(X); ~~[dsat(Y) 
sat(X)]~~                   | sat(Y) sat(X); sat(Z) dsat(X)
| `and_v(X,Y)`                 | *(none)*; ~~[dsat(Y) 
sat(X)]~~                          | sat(Y) sat(X)
| `and_b(X,Y)`                 | dsat(Y) dsat(X); ~~[sat(Y) dsat(X)]; 
[dsat(Y) sat(X)]~~ | sat(Y) sat(X)
| `or_b(X,Z)`                  | dsat(Z) 
dsat(X)                                         | dsat(Z) sat(X); sat(Z) 
dsat(X); ~~[sat(Z) sat(X)]~~
| `or_c(X,Z)`                  | 
*(none)*                                                | sat(X); sat(Z) 
dsat(X)
| `or_d(X,Z)`                  | dsat(Z) 
dsat(X)                                         | sat(X); sat(Z) dsat(X)
| `or_i(X,Z)`                  | dsat(X) 1; dsat(Z) 
0                                    | sat(X) 1; sat(Z) 0
| `thresh(k,X_1,...,X_n)`      | All dsats; ~~[Sats/dsats with 1 &le; 
#(sats) &ne; k]~~  | Sats/dsats with #(sats) = k
| `multi(k,key_1,...,key_n)`   | 0 0 ... 0 (k+1 
times)                                   | 0 sig ... sig
| `multi_a(k,key_1,...,key_n)` | 0 ... 0 (n 
times)                                       | sig/0 with #(sig) = k and 
#(sigs/0) = n
| `a:X`                        | 
dsat(X)                                                 | sat(X)
| `s:X`                        | 
dsat(X)                                                 | sat(X)
| `c:X`                        | 
dsat(X)                                                 | sat(X)
| `d:X`                        | 
0                                                       | sat(X) 1
| `v:X`                        | 
*(none)*                                                | sat(X)
| `j:X`                        | 0; ~~[dsat(X) (if nonzero top 
stack)]~~                 | sat(X)
| `n:X`                        | 
dsat(X)                                                 | sat(X)

#### Non-malleable Satisfaction Algorithm

In order to produce non-malleable satisfactions we make use of a 
function that returns the optimal
satisfaction and dissatisfaction for a given expression (if any exist), 
or a special DONTUSE value,
together with an optional HASSIG marker that tracks whether the solution 
contains at least one
signature. To implement the function:
* Invoke the function recursively for all subexpressions, obtaining all 
their satisfactions/dissatisfactions.
* Iterate over all the valid satisfactions/dissatisfactions in the table 
above (including the non-canonical ones), taking into account:
  * The dissatisfactions for `sha256`, `ripemd160`, `hash256`, and 
`hash160` are always malleable, so instead use DONTUSE there.
  * The non-canonical options for `and_b`, `or_b`, and `thresh` are 
always overcomplete, so instead use DONTUSE there as well (with HASSIG 
flag if the original non-canonical solution had one).
  * The satisfactions for `pk_k`, `pk_h`, and `multi` can be marked HASSIG.
  * When constructing solutions by combining results for subexpressions, 
the result is DONTUSE if any of the constituent results is DONTUSE. 
Furthermore, the result gets the HASSIG tag if any of the constituents does.
* If among all valid solutions (including DONTUSE ones) more than one 
does not have the HASSIG marker, return DONTUSE.
* If instead exactly one does not have the HASSIG marker, return that 
solution.
* If all valid solutions have the HASSIG marker, but all of them are 
DONTUSE, return DONTUSE-HASSIG. The HASSIG marker is important because 
while this represents a choice between multiple options that would cause 
malleability if used, they are not available to the attacker, and we may 
be able to avoid them entirely still.
* Otherwise, all not-DONTUSE options are valid, so return the smallest 
one (in terms of witness size).

To produce an overall satisfaction, invoke the function on the toplevel 
expression. If no valid
satisfaction is returned, or it is DONTUSE, fail. Otherwise, if any 
timelocking is used in the
script but the result does not have the HASSIG flag, also fail. If the 
satisfaction is both not
DONTUSE and HASSIG, return it.

## Discussion

## Security

Miniscript primarily aims to provide guarantees on the correctness of a 
Bitcoin Script. That is, to
guarantee **consensus soundness** and **standardness completeness**. 
Consensus soundness means
it is not possible to construct a consensus-valid witness for a Bitcoin 
Script unless the Miniscript
spending conditions are met. Standardness completeness means a 
standardness-valid witness can be
created for all spending paths of a Miniscript, assuming the resource 
limits are respected and there
is no timelock mixing.

Additionally, Miniscript can guarantee the non-malleability and maximum 
size of a witness. These can
assist in assessing the soundness of protocols where transaction fees 
(and therefore transaction
size) are security-critical parameters.

Hash preimages are constrained to 32 bytes to disallow various forms of 
griefing, including making
non-standard (un-relayable) transactions, consensus-invalid swaps across 
blockchains, as well as
ensure that satisfaction cost can be accurately calculated.

In order for these properties to not just apply to script, but to an 
entire transaction, it's
important that the witness commits to all data relevant for 
verification. In practice this means
that scripts whose conditions can be met without any digital signature 
are insecure. Besides being
trivially insecure, note how a transaction lacking a signature check 
allows an attacker to change
its nLockTime and nSequence fields to meet additional timelock conditions.

### Type system

To statically verify the correctness and malleability guarantees 
discussed in the previous section,
we define a type system. See the specifications above for a reference of 
each fragment's
requirements and properties. Here we give more information about each type.

Every expression has one of four basic types:
* "**B**" Base expressions. These take their inputs from the top of the 
stack. When satisfied, they push a nonzero value of up to 4 bytes onto 
the stack. When dissatisfied, they push an exact 0 onto the stack (if 
dissatisfaction without aborting is possible at all). This type is used 
for most expressions, and required for the top level expression. An 
example is `older(n)` = `<n> CHECKSEQUENCEVERIFY`.
* "**V**" Verify expressions. Like "B", these take their inputs from the 
top of the stack. Upon satisfaction however, they continue without 
pushing anything. They cannot be dissatisfied (will abort instead). A 
"V" can be obtained using the `v:` wrapper on a "B" expression, or by 
combining other "V" expressions using `and_v`, `or_i`, `or_c`, or 
`andor`. An example is `v:pk(key)` = `<key> CHECKSIGVERIFY`.
* "**K**" Key expressions. They again take their inputs from the top of 
the stack, but instead of verifying a condition directly they always 
push a public key onto the stack, for which a signature is still 
required to satisfy the expression. A "K" can be converted into a "B" 
using the `c:` wrapper. An example is `pk_h(key)` = `DUP HASH160 
<Hash160(key)> EQUALVERIFY`.
* "**W**" Wrapped expressions. They take their inputs from one below the 
top of the stack, and push a nonzero (in case of satisfaction) or zero 
(in case of dissatisfaction) either on top of the stack, or one below. 
So for example a 3-input "W" would take the stack "A B C D E F" and turn 
it into "A B F 0" or "A B 0 F" in case of dissatisfaction, and "A B F n" 
or "A B n F" in case of satisfaction (with n a nonzero value). Every "W" 
is either `s:B` (SWAP B) or `a:B` (TOALTSTACK B FROMALTSTACK). An 
example is `s:pk(key)` = `SWAP <key> CHECKSIG`.

Then there are 6 type modifiers, which guarantee additional properties:
* "**z**" Zero-arg: this expression always consumes exactly 0 stack 
elements.
* "**o**" One-arg: this expression always consumes exactly 1 stack element.
* "**n**" Nonzero: this expression always consumes at least 1 stack 
element, no satisfaction for this expression requires the top input 
stack element to be zero.
* "**d**" Dissatisfiable: a dissatisfaction for this expression can 
unconditionally be constructed. This implies the dissatisfaction cannot 
include any signature or hash preimage, and cannot rely on timelocks 
being satisfied.
* "**u**" Unit: when satisfied, this expression will put an exact 1 on 
the stack (as opposed to any nonzero value).
* "**k**" No timelock mixing. This expression does not contain a mix of 
heightlock and timelock of the same type. If the miniscript does not 
have the "k" property, the miniscript template will not match the user 
expectation of the corresponding spending policy.

Finally to analyze malleability guarantees we introduce 3 new type 
modifiers:
* "**s**" Signed: satisfying this expression always requires a signature 
(predicting whether all satisfactions will be HASSIG).
* "**f**" Forced: dissatisfying this expression always requires a 
signature (predicting whether all dissatisfactions will be HASSIG).
* "**e**" Expressive: this requires a unique unconditional 
dissatisfaction to exist, and forces all conditional dissatisfactions 
(if any) to require a signature.

### Malleability

Since Segwit, malleating a transaction no longer breaks the validity of 
unconfirmed descendant
transactions. However, unintentional malleability may still have a 
number of much weaker undesirable
effects. If a witness can be stuffed with additional data, the 
transaction's feerate will go down,
potentially to the point where its ability to propagate and get 
confirmed is impacted. Additionally,
malleability can be exploited to add roundtrips to BIP152 block 
propagation, by trying to get
different miners to mine different versions of the same transaction. 
Finally, malleability may
interfere with the usage of hash locks as a mechanism for publishing 
preimages.

Using the malleability type properties it is possible to determine 
statically whether a script can
be nonmalleably satisfied under all circumstances. In many cases it is 
reasonable to only accept
such guaranteed-nonmalleable scripts, as unexpected behavior can occur 
when using other scripts.

For example, when running the non-malleable satisfaction algorithm 
above, adding available
preimages, or increasing the nLockTime/nSequence values actually may 
make it fail where it succeeded
before. This is because a larger set of met conditions may mean an 
existing satisfaction goes from
nonmalleable to malleable. Restricting things to scripts that are 
guaranteed to be satisfiable in a
non-malleable way avoids this problem.

When analysing Miniscripts for resource limits, restricting yourself to 
just non-malleable solutions
(or even non-malleable scripts) also leads to tighter bounds, as all 
non-canonical satisfactions and
dissatisfactions can be left out of consideration.

The malleability analysis makes the following assumptions:
* The attacker does not have access to any of the private keys of public 
keys that participate in the Script. Participants with private keys 
inherently have the ability to produce different satisfactions by 
creating multiple signatures. While it is also interesting to study the 
impact rogue participants can have, we treat it as a distinct problem.
* The attacker only has access to hash preimages that honest users have 
access to as well. This is a reasonable assumption because hash 
preimages are revealed once globally, and then available to everyone. On 
the other hand, making the assumption that attackers may have access to 
more preimages than honest users makes a large portion of scripts 
impossible to satisfy in a non-malleable way.
* The attacker gets to see exactly one satisfying witness of any 
transaction. If he sees multiple, it becomes possible for the attacker 
to mix and match different satisfactions. This is very hard to reason about.
* We restrict this analysis to scripts where no public key is repeated. 
If signatures constructed for one part of the script can be bound to 
other checks in the same script, a variant of the mixing from the 
previous point becomes available that is equally hard to reason about. 
Furthermore this situation can be avoided by using separate keys.

#### Non-Malleable Satisfaction

Malleable satisfactions or dissatisfactions appear whenever options are 
available to attackers distinct from the one taken by honest users. This 
can happen for multiple reasons:
1. Two or more options for a satisfaction or dissatisfaction are listed 
in the table above which are both available to attackers directly. 
Regardless of which option is used in the honest solution, the attacker 
can change the solution to the other one.
2. Two or more options for a satisfaction or dissatisfaction are listed 
in the table above, only one of which is available to attackers, but the 
honest solution uses another one. In that case, the attacker can modify 
the solution to pick the one available to him.
3. The honest users pick a solution that contains a satisfaction which 
can be turned into a dissatisfaction without invalidating the overall 
witness. Those are called overcomplete solutions.

Because we assume attackers never have access to private keys, we can 
treat any solution that
includes a signature as one that is unavailable to attackers. For 
others, the worst case is that the
attacker has access to every solution the honest users have, but no 
others: for preimages this is an
explicit assumption, while timelock availability is determined by the 
nLockTime and nSequence fields
in the transaction. As long as the overall satisfaction includes at 
least one signature, those
values are fixed, and timelock availability is identical for attackers 
and honest users.

The description of the non-malleable satisfaction algorithm can be used 
to show that no
non-canonical solutions listed in the satisfaction table can occur 
inside non-malleable
satisfaction:
* Some of the non-canonical options (the `or_b`, `and_b`, and `thresh` 
ones) are overcomplete, and thus can clearly not appear in non-malleable 
satisfactions.
* The fact that non-"d" expressions cannot be dissatisfied in valid 
witnesses rules out the usage of the non-canonical `and_v` dissatisfaction.
* "d" expressions are defined to be unconditionally dissatisfiable, 
which implies that for those a non-HASSIG dissatisfaction must exist. 
Non-HASSIG solutions must be preferred over HASSIG ones (reason 2), and 
when multiple non-HASSIG ones exist, none can be used (reason 1). This 
lets us rule out the other non-canonical options in the table:
  * `j:X` is always "d", its non-HASSIG dissatisfaction "0" always 
exists, and thus rules out any usage of "dsat(X)".
  * If `andor(X,Y,Z)` is "d", a non-HASSIG dissatisfaction "dsat(Z) 
dsat(X)" must exist, and thus rules out any usage of "dsat(Y) sat(X)".
  * If `and_b(X,Y)` is "d", a non-HASSIG dissatisfaction "dsat(Y) 
dsat(X)" must exist, and thus rules out any usage of "dsat(Y) sat(X)" 
and "sat(Y) dsat(X)". Those are also overcomplete.
  * `thresh(k,...)` is always "d", a non-HASSIG dissatisfaction with 
just dissatisfactions must exist due to typing rules, and thus rules out 
usage of the other dissatisfactions. They are also overcomplete.

### Resource Limits

Various types of Bitcoin Scripts have different resource limitations, 
either through consensus or standardness. Some of them affect otherwise 
valid Miniscripts:
* In P2WSH, scripts larger than 3600 bytes are invalid by standardness. 
In Tapscript scripts are implicitly bounded by the maximum size of a 
block (1 million virtual bytes).
* In P2WSH, script satisfactions where the total number of non-push 
opcodes plus the number of keys participating in all executed 
`CHECKMULTISIG` is above 201 are invalid by consensus.
* In both Tapscript and P2WSH, script satisfactions which make the stack 
exceed 1000 elements before or during execution are invalid.
* In P2WSH, satisfactions with a witness consisting of over 100 stack 
elements (excluding the script itself) are invalid by standardness.

A static analysis can be performed on a Miniscript to verify if none, 
all or any of the spending
paths hit any of the limits.

## Test Vectors

TBD

## Backwards Compatibility

Miniscript's syntax is compatible with BIP 380 Output Script 
Descriptors, and should be considered
an extension to it that provides a new type of Script expression that is 
only valid in
`wsh()` and `tr()` contexts. As these are wholly new expressions, they 
are not
compatible with any existing implementation of descriptors. 
Additionally, the scripts produced are
unlikely to be standard scripts.

The `pk()`, `pkh()`, `multi()`, and `multi_a()`
fragments overlap with existing descriptors. These parse to the same 
semantic meanings as those
descriptors and produce the same scripts.

## Reference Implementation

A first reference implementation and documentation for Miniscript in 
P2WSH was originally published at
https://github.com/sipa/miniscript .

The reference implementation for Miniscript in P2WSH was introduced in 
Bitcoin Core through PRs
https://github.com/bitcoin/bitcoin/pull/24147 
https://github.com/bitcoin/bitcoin/pull/24148 and
https://github.com/bitcoin/bitcoin/pull/24149 . The last one to be 
merged was released in Bitcoin
Core version 25.0.

The reference implementation for Miniscript in Tapscript was introduced 
in Bitcoin Core in PR
https://github.com/bitcoin/bitcoin/pull/27255 . This PR was merged and 
released for Bitcoin Core
version 26.0.

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