Slides: https://www.dropbox.com/s/vgh5vaooqqbgg1v/andrew-poelstra.pdf

Hi everyone. Some of you were at my Bitcoin dev presentation about Miniscript a couple of days where I managed to spend over 2 hours giving a presentation about this. I think I got this one down to 20 minutes but no promises. I will keep an eye on the clock.

It is very nice having this scheduled immediately after Andrew Chow’s talk about output descriptors because there is a good transition here. As Andrew mentioned the way that the Bitcoin Core wallet used to work and still works is this bag of keys thing. You have a whole bunch of elliptic curve keys and these are interpreted in whatever way happens to be convenient at the time. This results in a messy user model and potentially weird things like the ability for third parties to manipulate addresses in unexpected ways. Descriptors solve this basically by being much more precise about the way that keys are supposed to be used and also by being more expressive. But as Andrew hinted there are more ways that descriptors could be expressive and that brings us into Miniscript. There are things like multisignatures, various multi key policies and it would be nice if descriptors could support now that we have some nice engineer readable representation of things.

There are a pile of use cases even for ordinary users. This is not necessarily things like Lightning or complicated protocols or anything where you might need multiple keys. Ordinary users who just want to have multiple redundant hardware wallets like Stepan (Snigirev) was talking about might want to use multisignatures. People who might want to have some backup key, some dead man’s switch where if they lose their hot keys after a time they can still recover their coins. That is a sensible thing to want to do. That would require a timelock or something. Then these things might also be embedded in some larger scheme. You can imagine somebody who wants to do this complicated multisignature for their own purposes but they are a participant in some larger scheme. Like they are in a split custody wallet, they have got some counterparty who is going to countersign all of their transactions. Maybe they would like to do something interesting and the counterparty hopefully shouldn’t have to be decoding weird scripts to understand what the user is doing. Or maybe they are part of a custody set or a board for a company that holds a lot of Bitcoin like Blockstream say. They have their own complicated multi key set up. Everybody who works at Blockstream has their own weird complicated multi key thing. Wouldn’t it be great if they could all bring their policies to the table and we could just combine those and have some threshold? We say 3-of-5 people or 8-of-10 or however many we can get. Each one of those individual policies was something complicated. These are the kind of things that are very difficult to do today because we don’t have a good way to represent complicated scripts.

The way that we do represent scripts is through this thing called Bitcoin script. I have been using this word script but what I am trying to hint at are spending policies. But the way it is implemented is Bitcoin script. Script can do all sorts of cool things. One interesting example is Peter Todd has some coins out there that can be taken if you can find a hash collision. There is one for SHA1 that has been taken. There are others for SHA2 and RIPEMD which have not been taken. That is a cool thing you can do with script. In practice what people typically do is they use script to check signatures with certain keys, they check for hash preimages for things like atomic swaps and Lightning HTLCs and they check timelocks for things like these dead man switches or backouts or claim a refund constructions. Then they compose these in various ways called monotone functions. A monotone function is just ANDs and ORs and thresholds. Putting things together into some tree of ANDs and ORs and thresholds.

Conceptually these monotone functions of various spending conditions, these are spending policies, they’re not really scripts, they’re not really programs that you are running. So you can imagine that if Bitcoin was differently designed you could directly encode a list of spending policies. I have given an example here in a suggestively descriptor like format.

(pk(A),or(pk(B),or(pk(C),older(1000))))

You could imagine having some sort of multisignature policy. We’ve got these three keys A, B and C. We have got a 1000 block timeout and we put them together in this way. Wouldn’t it be cool if you could put that into a descriptor? Then the question becomes how do you map something sensible looking like that into Bitcoin Script? That is where Miniscript is going to come in.

The idea behind Miniscript is that we can take a policy like that, we all have these components, keys, hashes and so forth and we map these directly into Script. We have these script templates which when executed do the required check. You also have these script templates that will work as ANDs or ORs so you can compose these. You can take a template that has a couple of gaps and fill in other script components, literally an encoding of these spending policies in Bitcoin Script. It is cool because conceptually there are two ways to read this. You can read this as a tree of ANDs and ORs or you can read this as a program to be executed on the Bitcoin blockchain.

To summarize this situation I am describing Script works by manipulating these opaque blobs of data. It is a very low level stack machine. You give it a bunch of objects, some of them represent booleans, some of them represent signatures, some represent public keys or hashes. Some represent numbers that you can add together, you can do various operations on them. It is really not thinking in terms of spending policies. The difficulty with the current situation is exactly this. The script model is this low level stack machine that doesn’t have any obvious mapping at all to the model that I am trying to describe where you have got a collection of different spending conditions. Miniscript as we will see does match this user model.

Let me summarize the problems with Script as I see them. A giant list of many problems that I see with Script real quick. When you are in this stack based, low level opcode model it is difficult to argue that your script is correct, that it is actually going to do what you expect. It is difficult to argue that it is secure meaning that it won’t do what you don’t expect. It is difficult to argue about malleability. That’s something I will talk about in a couple of slides. If you are a wallet implementer you run into problems with fee estimation. It is difficult to estimate how large a witness might be when you are satisfying a given script. It is difficult to know if you have got multiple parties involved which public keys require signatures, how many signatures you need and do you require hashlocks and do you require a certain timelock to be signed and so forth? Even if you can figure out that data, figuring out how to assemble it into a witness is non-trivial because Bitcoin Script has a lot of different opcodes that require different things in different orders and in different formats. If you are trying to write software that could work with arbitrary scripts you’ve got quite a difficult program analysis on your hands.

These problems with Script directly translate into problems for designing something like Miniscript. The idea is that I can just encode my spending policies as scripts. But scripts have these problems in designing these fragments, these templates. One is there are many ways to write every fragment. If I am trying to do a public key check I can use a CHECKSIG operator, I could use CHECKSIGVERIFY operator which is slightly different semantics. I could use the CHECKMULTISIG operator and throw a single public key in there or something weird like that. There are three ways to write a pubkey check. The CHECKMULTISIG one is obviously inefficient. There is no reason to do that but the other two might be usable in different contexts. It is hard to composes these fragments. The CHECKSIG operator if it succeeds will put a 1 on the stack, if it fails it will put a 0 on the stack. CHECKSIGVERIFY if it succeeds will put nothing on the stack and if it fails it will abort the script. So if I am trying to write a script fragment that represents a boolean AND or a boolean OR I need to consider that for some things I plug in I’ll have a 1 or 0 sitting around and for other things I plug in I won’t. Maybe I need different kinds of AND and OR fragments that can handle these different possibilities. There is a design problem here and there is an analysis problem of making sure that the actual composition of fragments that a user comes up with is something sensible. Another constraint is that I can’t just throw away every fragment except for one. I can’t do something silly, inefficient and simple because cost is really critical here. Every byte matters here. As Monty Python said “Every byte is precious” on Bitcoin. Users really care about the size of their scriptPubKeys, they care about the size of the witnesses that they produce to spend their coins and those are actually two different things. When they are composing things they may care about the size of the witness if they are not satisfying something. If you have got an OR of two different branches, maybe you satisfy one but dissatisfy the other. There are all these different cost dimensions when considering the size of fragments. When you are designing a Miniscript you need to consider for every fragment how likely it is to actually be satisfied, how likely it is to be dissatisfied and how likely it is to be skipped completely over if it is a IF branch that doesn’t get called. This means that there are trade-offs. You can’t just pick one fragment that is obviously the best. Even if you know what your policy looks like there is not one fragment that is obviously the best. You really need to support all these different fragments and you need a way for the user to verify that what they are doing is not only sensible and not only efficient but actually the most efficient thing for the specific use case that they are considering. A final point on this slide is actually getting an optimal script might involve some funky things. If you see the same public key occur twice then maybe you want to rearrange it so it only occurs once. You completely restructure what your predicate looks like. That is out of scope for Miniscript. Doing whole program optimization things like this would be cool and in theory it is possible but it breaks this nice, simple user model where you’ve got a tree of spending conditions and you produce a policy that way. If you are doing any advanced manipulation on these things then we would lose that simple engineer readable, easy to reason about, easy to check consistency properties.

Then let’s get into malleability. Beyond thinking about correctness which in some sense is a straightforward engineering problem and about optimality which is also in some sense engineering, we have this issue of malleability. This was a really hot word before SegWit was around. First of all what malleability is is the ability for some third party given a Bitcoin transaction to replace the witnesses with some other witnesses that are also valid. You get a different transaction that still does exactly the same thing, it is still a valid transaction but it is different in some way. Before SegWit this was really serious because the witnesses would go into the transaction ID so if you were chaining multiple offchain transactions this third party would break the whole chain and you were in a lot of trouble. Post SegWit malleability is still a thing, it is no longer a protocol breaking thing but it is an efficiency thing in two big ways. One is that it can affect transaction propagation properties. If somebody changes out a witness and some nodes have seen a transaction with one witness and others see a transaction with another witness one of those is going to get into a block and this can interfere with compact block reconciliation. At some point you do need the full witness and stuff and if your node is surprised by what the witness in the blockchain turns out to be that is an inefficiency for the network. From a user perspective if there is potential to replace a witness with a larger witness that means that your transaction as it hits the network is larger than the transaction you created and so the fee rate that the network sees is lower than the fee rate you set. Now you are surprised by your transaction having a lower priority than you wanted it to. This is actually potentially a security issue because it means that your transaction might not propagate when you expected it to. Or it might not be accepted into people’s mempool when you expected it would be.

So to make the task of designing Miniscript tractable we set a few design rules here which more or less I have already said. The first is that we are going to assume the standard Bitcoin Core mempool policy rules. Standardness is the term we used to use. The reason we do this is that there are a lot of anti-malleability things in Core’s policy rules that are not in Bitcoin’s consensus. One prominent example of this is that there is an IF opcode in Bitcoin. If you give it a 1 it will do the thing, if you give it a 0 it will not do the thing. There are many, many ways to encode 1, there are many ways to encode 0. If you have a script that is using this OP_IF and you provide a 0 or 1 in your witness, in principle some third party could change that 0 into a 0 that is twenty zeros in a row. Or could change your 1 into any nonzero value or something like that and make your transaction bigger and then you are in trouble. You can prevent this, you can make the transaction invalid in this case by using this trick. You use OP_SIZE followed by OP_EQUALVERIFY. This is the one little bit of Bitcoin Script that I am going to throw in here. SIZE EQUALVERIFY is a really cute trick. SIZE puts the size of your top most stack element onto the stack. EQUALVERIFY checks the two things are equal. What SIZE EQUALVERIFY does is if your top element on the stack is equal to its own bit size that’s great. If its not it will fail the transaction. As it turns out in Bitcoin Script there are only two values that are equal to their own size. That is 0 which is the empty string which has size 0 and 1 which is the byte 1 that has size 1. We could put SIZE EQUALVERIFY in front of every single IF and we could also put extra validity checks and length checks in front of all our signature checks for example. There are a bunch of other guards that we could put into all of our script fragments but we don’t want to do that because we are wasting bytes there. In practice this is not really an issue because the network is so overwhelmingly enforcing these policy rules that really only miners could exploit this kind of malleability. Miners already have the ability to mess with transactions. If miners want to hurt network propagation they can just produce a whole bunch of transactions that no-one has seen before and stuff blocks full of these. Now compact blocks doesn’t work. Miners already have the ability. The problems with malleability are already things that miners can do so we are going to stick with policy rules. As I mentioned we are not going to try any common subexpression elimination, we are not going to try to manipulate our program, we are not going to try to rearrange things. First of all this is very difficult in general to find the optimal encoding of a program. Secondly it breaks analyzability. Then also we are going to assume for the purpose of automatic reasoning about malleability, which is something we do in Miniscript that I will touch on but not go into too much detail, we are going to assume that people’s keys are not reused within a specific script. The reason for this is that if somebody uses the same key twice then if they sign in one branch, a third party could see that signature and copy it and use it in a different branch. This potentially introduces a malleability vector where otherwise there wouldn’t be one. This is very difficult to reason about in automated ways. You have really got to know which branches are disjoint from other branches. In general it seems like an intractable problem. We also assume no key reuse for the purpose of fee estimation. This appears in some edge cases when you are thinking about how to estimate witness size. We are going to throw that away for the purpose of having something that we can describe and we can deploy.

The final design thing in Miniscript that we are forced into is to separate out this notion of the Policy language that is something that I showed you several slides ago where you’ve got these ANDs and ORs and so forth, from Miniscript itself. The idea is that Policy language is high level, that is the engineer or maybe even user readable thing. It directly describes which spending conditions are available and in what combinations. In these policies we also allow labelling different branches with different probabilities for certain branches being taken. This allows us to take a policy, compile it down to a Miniscript and make choices about which specific script fragments we want to use based on the likelihood of certain branches being taken. We get a lot of optimization ability here. We have this Policy language, kind of high level. This is distinct but very similar to Miniscript itself which I am going to show you in the next couple of slides. Miniscript really does directly correspond to Bitcoin Script. It is an alternate encoding of a subset of Bitcoin Script where this encoding is clearly a tree of ANDs and ORs and thresholds. We have Miniscript itself which really is this re-encoding of Script. The difference between Miniscript and the Policy language is first of all there are no probabilities in Miniscript. Secondly in Miniscript we explicitly label which fragments we are using in all cases when there are multiple options.

Let me show you what this looks like. Here is an example of a policy. Rather than writing it in the string descriptor format I have the ability to draw these nice pictures. This is the cool thing about Miniscript that you can’t do with regular scripts. Conceptually what I’ve got is this tree of objects rather than having a bunch of instructions for a stack machine. I get this nice format. Here is the policy. You can see I’ve got four keys going around, I’ve got a hash preimage, I’ve got a timelock. There is various analysis I might want to do on this policy. Say I am the owner of public key 4 (pk_4) on the right there and my job is to be a countersigner. I don’t really care what else is going on here. What I want to know is can this script be spent without my permission, without me signing off on it? Or after the coins have been sitting still for a 1000 blocks maybe I am willing to back off. I can easily go through this and say “Do there exist any ways to spend this where my key does not appear?” Let’s go through all of the spending possibilities. The top level I have this AND so both of these need to happen. On the right hand side I have got an AND so both of these need to happen. The only way to spend these coins, I can immediately visually see that both of these branches are satisfied. I can see that one of them is exactly the policy that I want. So I know without a doubt that there is no secret way these coins can be spent out of my control even though I didn’t look at most of the script. All I did was run through the branches and check there existed one in every possible spending path where my key was involved or this alternate timeout.

Here is what a Miniscript looks like. These are almost the same picture. You can see that the difference here is that in Miniscript I have labeled all the ANDs and ORs and things with specifically which script fragment I want to use. I have also labelled them with B’s and V’s, there are K’s and W’s too. These represent types which I am not going to go into in this talk. Miniscript has a type system that allows automatic verification of correctness. Then I have also got these c’s, vc’s and jv’s and stuff. What these represent are script fragments that don’t really have any semantic meaning but they allow me to encode things in a more efficient way. v for example means that you add an OP_VERIFY at the end of something which turns a 1 or 0 result like what CHECKSIG does into a pass, fail result like what CHECKSIGVERIFY does. v means put a VERIFY on it. j is this weird wrapper where we look to see whether or not the user has given us zero. If the user has given us zero we skip over whatever we are wrapping. If they give us a nonzero we pass that as the input to the fragment. The reason we do this is for a hash preimage we want to give the user the option either to provide a valid hash preimage or to provide the byte string zero which means skip over this, fail the check. This j wrapper gives us exactly those semantics. You can see that has nothing to do with the policy but it is clearly important for actually encoding things as Script. At the bottom here I have got the actual Bitcoin Script and opcodes. That is what it looks like.

For time reasons I am going to skip over this slide. Basically one of Andrew’s (Chow) projects is PSBT which is an unsigned transaction wallet interchange format. Miniscript was designed to work with PSBT. They both make each other more powerful. There are some very generic multi wallet tooling that we can write using the one-two punch of Miniscript and PSBT. That is all I am going to say here.

Let me quickly advertise my workshop and then I will wrap up. Tomorrow morning I am doing a workshop 9:30 to 12:30. Unlike the other workshops here this is not going to be super programming focused. The reason being that my Miniscript library is written in the Rust programming language and I don’t think it is reasonable to expect people to either already know Rust or to learn it in the next couple of days. It has a very high learning curve famously. There is a Python implementation that James Chiang wrote but I don’t think it is quite finished. It is a PR to Bitcoin Core as part of the Python test framework. It is not quite finished and I haven’t looked over it and I don’t really know how to use it. That would be a good thing to use for a workshop but we don’t have access to it. Instead I am going to do something a little bit more theoretical. We are going to go through a lot of the weird oddities in Bitcoin Script. Maybe we will look at interpreter.cpp which is one of the weirdest and oldest files in Bitcoin Core and see some of the weird things the script interpreter does that might confound various kinds of analysis. We will look in more depth at things like correctness and malleability and surprising foot guns that you encounter when working with Script. Even when working with Miniscript there are surprising things that sometimes the Miniscript type system can catch for you but nonetheless they are often non-obvious and subtle things. Over the course of development I often would try to do weird things with Miniscript and my code would refuse to sign for transactions, it would reject it somehow. I think the code is broken but when I trace through the way it was failing, it was showing me that there was some malleability vector in what I was trying to do. There was an actual attack that I had not considered. It is really cool we can do this in an automated way because this is really subtle stuff and really foot gunny and non-obvious.

To wrap up, there is this thing called Miniscript. It makes spending policies as encoded in Bitcoin Script. Human readable, let’s say engineer readable, I like Andrew’s term. And machine analyzable. We can do all sorts of cool things, in particular things like constructing witnesses, determining what keys are required, estimating witness size even under certain constraints. These become tractable and in fact we can do this in a very generic way where somebody like me could write some code that does this and then everyone could just use it. We are no longer reinventing the wheel for every single individual weird policy. You also get this composability thing that I mentioned way back at the beginning of the talk. If you have got some larger Miniscript as we saw with the picture I can take some little fragment that I care about for my purposes and not really care about what the other participants are doing as long as the overall script is using my policy in the way that I want it to. We get this composability where I can participate in custodying the coins that Blockstream controls say, and I show up to the table with some crazy multisignature timelocked whatever thing and all everyone else needs to do is that is me. Somehow that big blob is me. They know that I haven’t somehow backdoored it by doing this complicated thing. All I need to know is that I am contributing. You can’t move the coins without me or some large number of people. We will go into this in a fair bit more detail tomorrow morning. Thank you all for listening.

Q - You were saying there was a problem with public key reuse. Have you thought about using the very non-famous OP_CODESEPARATOR operator which allows you to really use only one public key for one person but sign a specific branch of your script?

A - This is a really cool question. The question is about using OP_CODESEPARATOR which is this obscure opcode that lets you basically tag what you are signing in a technical way so that a signature for one part of your script can’t be reused for a signature in another part of your script. First off this is a little bit inefficient. We are adding extra bytes by sticking these OP_CODESEPARATORs in places. Some users maybe don’t care about this. Secondly this actually doesn’t cover all the cases that we might care about for technical reasons but that I can maybe go in tomorrow. You can imagine a threshold policy where you have 3-of-5 participants say. There are 5 choose 3 different ways you can spend this. You can imagine one person signs using the first three signers. Then somebody changes it to use the last three. Now the middle signer is in both cases. But OP_CODESEPARATOR because it only appears once on that key won’t be able to detect this kind of change in witness. So in that example this probably doesn’t matter because this is not an example of key reuse. But you can imagine a threshold policy that is more complicated. You can imagine a threshold of thresholds, something more elaborate, where this does actually matter. I have a few examples of these just not in my head right now.

Q - When you talked about j you said that perhaps the user wants the script to fail. Why would they want that, just not send the transaction?

A - You never want the whole script to fail but you may want some specific subsets of your script to fail. If you have an OR, one way that you can do an OR in Bitcoin is you can run a script fragment, you can store the result, it will be 0 or 1, throw it on the altstack say. Then you run another fragment and you store that 0 or 1. Then you pull the two results out and you run the OP_BOOLOR operation on that. The expectation is that whichever branch the user takes they are going to fail one of the two things and succeed the other one. This may actually be more efficient than doing it other ways using like OP_VERIFY or something like this. In that case you have a subset of your script that you do want to be able to fail. You want it to put a 0 on the stack that you then run through OP_BOOLOR to get a 1 and pass the larger script. That is why. Whenever you have conditionals is why you might want to fail stuff.

Q - So Andrew Chow said in the previous talk that output script descriptors describe everything you need to solve them. Does that mean there is redundancy between descriptors and Miniscript currently as they are designed?

A - No there is not redundancy. What output descriptors describe is where do you put the witnesses? If you have a PKH or something you just throw a signature into your scriptSig. If you are using SegWIt you put your witnesses in the witness field. If you are not using SegWit you put it in the scriptSig. That kind of stuff. What Miniscript describes is how you construct those witnesses in the first place. They complement each other. Output descriptors as implemented or as on the immediate roadmap for Core actually don’t support all of these advanced things that Miniscript does. They only support I think basic multisig and then all the different ways you can use single signer keys. What Miniscript gets you is the ability to do way more stuff with output descriptors. But the two parts that they do are disjoint, they are complementary.