https://twitter.com/kanzure/status/1091116834219151360

Jeremy: Our next speaker really needs no introduction. However, I am obligated to deliver an introduction anyway. I'm not just trying to avoid pronouncing his name which is known to be unpronounceable. I am pleased to welcome Pieter Wuille to stage to present on miniscript.

Thanks, Jeremy. I am Pieter Wuille. I work at Blockstream. I do various things. Today I will be talking about miniscript, which is a joint effort between myself and some colleagues at Blockstream particularly Andrew Poelstra.

Before I start, I want to tell you what this is not about. I recently released a software library called minisketch which is completely unrelated to this. I hope people were not expecting me to talk about minisketch. This is also not about any future soft-forks or research into improvements for bitcoin consensus layer. This is all about stuff avaliable and ready today, and it's very practical focused.

I'll talk about the problem, and show you this is a problem space of contracts and scripting that has been overlooked. Then I will design a policy language for describing things in bitcoin scripts, mapping it to bitcoin script and describing how to spend it, and then concluding with some future work.

At the very high level, bitcoin script is a forth-like stack based language, it has no loops, it is not turing complete and this is by design. It is untyped. Bitcoin has unspent transaction outputs, it's a UTXO model. Every coin is associated with a script. That script defines the conditions under which that output can be spent, and they are always spent in their entirety. Really the ability to spend an output in bitcoin is finding an input that makes this particular script in this scripting language evaluate to true. That's it. When you can do so, you can spend the output.

Unfortunately this language is pretty hard to reason about and use, despite being around since bitcoin's creation 10 years ago. There's really not all that many interesting scripts being used. I'll give some reasons for why that might be the case.

When thinking about script, we want something that is of course correct, that it is size efficient because size efficiency translates directly to low cost on chain, and we also want to avoid malleability. Despite having upgraded to segwit a while ago which removes most of the concerns around malleability, there's a few reasons still why you may want to avoid malleability still.

A simple example is that a specific public key must sign off. This is what most addresses in bitcoin encode. It's not the only possibility, though. There's also escrow like multisig or 2-of-3 thresholds where you put coins into escrow under condition that a third-party escrow agent says that whenever 2-of-3 agree then the money is released. The sender sends the money to the 2-of-3 threshold policy or script encoding the policy of 2-of-3 required and then the escrow can agree to which of the two it goes. The escrow on its own cannot itself run away with the money by itself.

There are other possible conditions, like 2-of-3, where after some time you have a timeout built into the script. A common script used in other constructions are HTLCs where you have two keys and a hash preimage is revealed allowing a spend, or after some time just some key can spend.

Really, this seems to be what bitcoin script can do. It is boolean operations over keys, times and hashes. The language seems a bit overcomplicated for actually just being able to do this.

In particular, something that I want to focus on in this talk is composability. Say you have the example of a company wants to store its funds in a 3-of-4 multisig construction where a number of employees or directors of the company need to sign off for spending. But one of the participants already has a fancy hardware setup construction that has a timelock built in, maybe a multisig of its own with a cold storage key. Why can't that setup as a whole, be one of the participants of those 4 members? This seems like a very natural thing you would want to do. If I am confident about protecting my own funds, then why should I be forced to stick to a small number of pre-defined policies?

The goal of what I am trying to achieve here is take any policy and within that policy be able to replace any key with another policy. So this is composability. This itself is an interesting goal. Practically speaking, the hardest part is how do you let software and hardware which are designed for different policies actually interact and accomplish this composability goal?

I want to point out a tool called Ivy. I think the author had a talk earlier today here. Tools like Ivy do help you construct more complicated scripts already, but I don't think they really give you a solution for the composability problem. When we're talking about this, you may think well really designing a new script that only happens very rarely when someone designs a new protocol or a new application on top of bitcoin and so on. But if we want composability, then this is no longer the case anymore and maybe it's something you need to do on a continuous basis.

I will start by designing a policy language to just describe the kinds of things I am talking about here. In bitcoin, the primitives are that you can spend with a public key which I will write as pk(KEY). Then there's multi(k,key1,key2,...). Then there's time(T) or hash(H) where the hash preimage needs to be revealed.

I'll use a thresholdconstruction where the arguments aren't keys anymore, but they are subexpressions. I have three specializations. One of this is just and(expression1, expression2) which is 2-of-2, and then two versions of or. The reason for this is that the second one (asymmetric or) is the asymmetric or whose goal is to express that the first subexpression is much more likely to be expressed than the second. I'll talk more about the probability model and how this lets you do actual optimization for minimizing the cost under certain circumstances.

I want to point out that nowhere here am I talking about witnesses. There are no signatures in this language. The preimage never appears. It is not really something that computes anything. It is really a combinator language for designing conditions, and that's all. This lets us choose the most efficient way of expressing how things need to be spent at a later stage.

Here are some examples of what we can do with that. Here's one with pk(key). I am not going to write everything out in hex. But in the real language, every time you see a letter on this slide, you will have to provide a key. Another example is escrow: multi(2,A,B,C). Another example is a vault which can be written as aor(and(pk(A),time(T)),pk(B)). HTLC can be written as aor(and(pk(A),time(T)),and(pk(B),hash(H))).

A 2-of-3 within 3-of-4 can be written as thres(3,pk(A),pk(B),pk(C),multi(2,D,E,F)).

I think this covers most of the expressions that is possible. But hash collisions are something I can't represent in this language.

If you are at all familiar with recent work in Bitcoin Core about output descriptors, you may see some similarity. This is justified because I plan to treat this as an extension to the descriptor language in Bitcoin Core for expressing all knowledge about how to spend a particular outputs.

So how are we going to map this to bitcoin script? The basic construction is pretty simple. You treat every subexpression as part of the script sequence of opcodes that expect its inputs, so its signature or whatever is expected from the top of stack and replaces it with a 0 or 1 at the top of the stack.

• pk(A) turns into <A> CHECKSIG.
• multi(2,A,B,C) turns into 2 <A> <B> <C> 3 CHECKMULTISIG.
• and(X,Y) turns into <X> TAS <Y> FAS BOOLAND.
• or(X,Y) turns into <X> TAS <Y> FAS BOOLOR.
• thres(2,X,Y,Z) turns into <X> TAS <Y> FAS ADD TAS <Z> FAS ADD 2 EQ.

TAS stands for "to alt stack" and FAS stands for "from alt stack". During execution, you have access to two stacks but the only operation you can do is move something from one stack to the other. So you have an alternate stack and the stack.

What if I were to want a 2-of-3 multisig for a number of keys, but then also require a 4th key D to always sign? Following the naive execution scheme I had before, this would turn into a rather long script. If you have looked at the semantic of script at all, this is really unnecessarily long. The way we went about improving this is by realizing that we could convert these subexpressions using different "calling conventions". In what way does it expect inputs on the stack and how does it return?

The original one which takes its input from the top of the stack and puts a 0 or 1 instead, is what I call the "E" calling convention. Another one that I am introducing is "W" which stands for wrapped. This is a version of converting to script where you expect the inputs to one below the stack. You expect something and the top of the stack you leave untouched. For almost all constructions we have, the wrapped version is the same as the other version but it has two .... It accomplishes that goal, but for a single checksig with a single key this is overkill and we don't need to move to the alt stack, we can just swap the two inputs because we know you are only going to consume one.

Doing this for every construction in the policy language, we now have two versions an E version and a W version and the argument to threshold for example invoke the wrapped version instead.

Another improvement we can make is realizing that the overall script at the top must always succeed. This is by definition, because it will only run when you actually satisfy it. When you have something that always succeeds, we can find more efficient versions of that code.

The "C" calling convention always aborts or succeeds. If you for example have an AND at the top of your policy, you can really just compile the first argument as a V version and the second version as if it was at the top again. This again lets you make more optimizations. The result here is something significantly shorter.

Remember I told you the policy language does not describe the actual encoding of the witnesses. What you put on the stack we can decide later. There are a whole lot of ways you can write an or() statement. The one I showed you before was a parallel OR where you run both and then do a boolean combination. But this has the downside that you have to provide inputs to both, even knowing that only one of the two will succeed.

There's an alternative called the cascade OR. You run A, and if it returns true then it returns 1 and else you run B. This means you no longer need to provide inputs for B if A is going to succeed.

There's also switching, where you can introduce an extra argument (an extra witness) that tells you whether A or B is the one that is going to succeed and then you can only provide one and be fine.

You can go further with conditional switching where you say if the whole expression will succeed and if it's not going to then I am not going to give you the inputs anyway.

I am trying to avoid malleability. The problem is that if you look at the switching OR, there's really two ways of making it not succeed. I can tell you A is the one that is going ot not succeed and then give you an input that does not satisfy A, or I can tell you B and then give an input that does not satisfy B. This leads to malleability because it's presumed to be easy to find inputs that don't satisfy certain conditions. In order to solve that, we need to introduce yet another calling convention, which puts 1 on the stack but under no circumstances can produce a 0.

Yet another step is what if you have a if-then-else with a CHECKSIG operator in both of the branches? It would be nice if we could move the CHECKSIG out. In order to deal with that, there's yet another calling condition where instead of immediately evaluating CHECKSIG, we leave a public key on the stack with which we expect a signature to happen. Through that convention, we can optimize here and there a few extra opcodes.

The reason why these things matter is because different scripts have different tradeoffs between satisfaction and how big non-satisfaction is and how big the script is. Sometime syou can find longer scripts that need less inputs, and so on. Depending on the probabilities of something getting executed at all or the probability of success, you might want to pick a different script.

If we look at all of those things, we end up with 6 calling conventions for all of the policies we came up with. We came up with 58 combinations of semantics and calling conventions, including 14 ways of expressing an OR. We pruned many. The result is a subset of script we call Miniscript.

It seems reasonable efficient. In particular, we did find slightly better scripts using it than a hand-written one that we were using in Blockstream Liquid. I don't know if we have adopted it yet.

There's a few limitations. Due to our composability construction, certain opcodes are really not usalbe. In particular, DEPTH, which tells you how big the stack is. Clearly its semantics change too dramatically when you compose things. It's possible that more efficient scripts exist that use DEPTH, but we wont find them. Also, we have no efficient way of doing CSE (common subexpression elimination).

We also found an efficient algorithm to find the most efficient miniscript given a particular policy. It is the exponential in the number of nested ORs. In practice, that's pretty usable.

http://bitcoin.sipa.be/miniscript/miniscript.html

We also have a rust implementation. While writing this compiler, we ran a competition between Andrew Poelstra and myself. We tried to figure out who can come up with the more efficient one. In the end, we found that we had significant flaws in our constructions and it eventually converged, so that's good.

So far I have only really addressed dealing with constructing a script that is a composition of certain policies. But my original goal was more ambitious: how can we make different tools designed for different policies to interact? To explain that, I am going to start with talking about Andrew Chow's bip174 partially-signed bitcoin transactions. It's a key-value format with metadata with all the information you need to figure out how to sign the transaction and if necessary if it's a p2sh output it will tell you the reedemScript, you can encode bip32 HD paths that keys are derived from so that a hardware wallet can derive them on the fly, etc.

There are 6 different roles associated with PSBT implementations. There's a creator that creates transaction templates, an updater that fills in information, signers that have access to private keys and can produce signatures, a combiner that combines them, a finalizer and extractor that produces a complete transaction. In practice, many of these roles happen simultaneously.

In the typical PSBT workflow, it's really only the updater and the finalizer that need to understand anything about the input scripts. This is somewhat surprising. It does make sense because when signing you generally care about where the money goes not whether it was already yours. Worst case, it's not yours and your signature would be invalid.

An obvious way of thinking about it is, well, we have a nice annotated policy form. So we could store it in the policy record in PSBT, and then others could actually sign. Actually this doesn't seem to be necessary, because not only is our policy language composable, but the subset of script is also composable. What this means is that you can actually, there's a very simple parser that you can write that given a script it will tell you the policy again. This means that we really don't even need to add any metadata to a PSBT to enable integration with it. This is somewhat of an artificial restriction, we could very much propose an extension for that, but overall it doesn't seem like we would gain that much by using a non-parseable or non-easily parseable script instead.

How do we imagine interaction to work? Scripts can be easily parsed back into an annotated policy, from which you can figure out which subsets of keys can sign. You can figure out what the policy does, and you can verify a policy ius a composition of a desired policy with another, and the composition is always sound. You can assemble a fully signed transaction from the signatures.

The origin of this is from a discussion on signer logic for the rust-bitcoin library. We were wondering what to do for signing, and someone was very much against a template-based signing where you say these are the few types of scripts we support and only these are the ones that are supported. So we went on this roundabout way to design this thing and in the end we decided that really the language to describe the structure of a script can be the script itself as long as it is within this subset that we call Miniscript.

I want to conclude by saying bitcoin script is mostly useful for simple policies but there's a lot more possible than what it is being used for. This is partly because it's hard to make things interact well. This sort of interaction could over time mean letting things like lightning client and a multisig client trivially interact without needing to read through all the protocol work. I'm not an expert on those details here.

We can define a subset of script which can be generically signed for, can be constructed easily, and can be analyzed easily, and as long as we don't have common subexpressions it's reasonably efficient for many use cases.

In the future, we need to open-source our implementations of the compiler and the parser. Right now the javascript compiler in the demo is not what you want to look at. Also, we want to integrate generic signer in common wallet software so we can immediately support PSBT or others. It could mean that I have a hardware wallet not even designed for these things but it will probably not give you a useful address in what is going on but at least some of them will likely support this without needing to know. And there are further optimizations that could be used to improve this. We used a relatively exhaustive approach to find all constructions but there's a whole bunch of things possible in script that we're not using.

We can use lessons learned here for future improvements... only if there was an OP_ROLL_BACKWARD that rolls in the other direction, you could precompute a value that would be used multiple times and just re-insert into the stack. This is the only time that I will be working other ongoing work like future improvements to bitcoin scripting like taproot and MAST, which can both directly reuse the policy language. The annotations will be different, but this should make upgradeability easier as well. You can write the policy now, and in the future it will be translated differently in a future script version.

Thank you.

Jeremy: Thank you very much. We have time for questions.

Q: Why not call the subset of script, subscript instead of miniscript?

A: I am I think notoriously bad at naming things. Originally I wanted to call it descript because it's script with something removed from it, and it interacted with our work on descriptors and people found it too confusing.

Q: Since you can't reuse witness arguments in different expressions, you can't do p2pkh in this?

A: Yes.

Q: If you were to extend this, I think you could add ... things that would make it easier to reuse arguments. Is there a way to do that while still preserving composability?

A: I would like to hear your opinions on this. In particular, about pubkeyhashes. In an earlier implementation, we had a pubkeyhash construction but if you think about it as expressing policies... the policy that a pubkeyhash implements is the same as the one, you do a hash at the top but there's really no reason why you would want a hash inside. Reusing witness things... we do have, say the wrapped W version of the hashlock. We found that actually the most efficient and really the only way you would want to do it if you also want to include a guarantee that the maximum size of the preimage is 32 bytes otherwise you might not be compatible across chains, then this is something that just takes a single argument whose size 0 refers to nonsatisfaction. So, there is a limited reasoning on reusing arguments in various places but they are all encapsulated within a particular combination of... I'm sure this can be improved.