Home < MIT Bitcoin Expo < Mit Bitcoin Expo 2020 < Taproot


Speakers: Andrew Poelstra

Date: March 7, 2020

Transcript By: Michael Folkson

Tags: Taproot

Category: Conference

Media: https://www.youtube.com/watch?v=1VtQBVauvhw

Topic: Taproot - Who, How, Why

Location: MIT Bitcoin Expo 2020

BIP 341: https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki

Intro (Hugo Uvegi)

I am excited to introduce our first speaker, Andrew Poelstra. He is coming to us from Blockstream where he is Director of Research. He is going to be talking about Taproot which I think is on everybody’s mind these days.

Intro (Andrew Poelstra)

Thanks for waking up so early for the first day of the conference and making the trek from the registration room over here. It is more faces than I expected considering. Hello to all the livestream people hiding from the Corona virus. I hope it doesn’t reach you, best of luck. I told myself I was going to write my slides on the plane. As you can tell I instead spent the entire plane ride drawing this title slide. I am very proud of. I hope you enjoy it. I am going to split this talk into two halves. I have only got 20 or 30 minutes. I can’t really describe Taproot in full detail in half a hour, probably even in a couple of hours. Instead I am going to give a brief overview of what Taproot is, describe some of the technical reasons for it being what it is and give a high level summary of the components of it. In the second half of the talk I am going to talk more generally about how we design proposals for Bitcoin, the considerations we have to make for a system with such high uptime requirements with so many diverse stakeholders who all more or less have a veto over proposals but nobody has the ability to push things through. And where everything is very conservative. We are all very afraid of deploying broken crypto or somehow breaking the system or causing a consensus failure or who knows what. Let’s get into it.

What is Taproot?

First half, what is Taproot? Taproot is a proposal for Bitcoin that was developed originally by Pieter Wuille, Greg Maxwell and myself. It has since been taken up by probably 10 major contributors who have been doing various things on IRC and on the mailing list over the last year or two. It is a new transaction output version, meaning that it is a new to define spending conditions for your coins on Bitcoin. I am going to talk about what that means.

Spending Conditions: Keys and Scripts

First off for those who don’t know Bitcoin has a scripting system. It has the ability to specify spending conditions on all of the coins. Typically for casual users the way we think of Bitcoins, you have an address, the address represents some sort of public key. You have a secret key corresponding to the public key and if you can produce a signature with that secret key you can spend the coins. This is actually a special case of what Bitcoin can do. It is not just one key, one signature kind of thing. We have the ability to describe arbitrary spending conditions where arbitrary means specifically you can check signatures with various public keys like you do with the normal one key standard wallet. You can check hashlocks which means you can put a hash of some data on the blockchain and it will enforce that somebody reveals the preimage of that which is a way to do a forced publication of some shared secret say. It can do timelocks where it won’t allow coins to move until some amount of time has gone by. You can do arbitrary monotone functions of these. You create a circuit out of ANDs and ORs, threshold 2-of-3 or 5-of-10 of these different checks. You can do arbitrary sets of these. The mechanism for these is called Bitcoin script. Script can do a fair number of other things, most of which are not super exciting. It can’t do a whole bunch of things. In particular you can’t use Bitcoin script to enforce things like velocity limits. A common thing people want to do is have a wallet where they have some coins that say only a certain amount of coins are allowed to move in a given day. That kind of thing you can’t do with Bitcoin script. For people thinking about future research directions for Bitcoin this the kind of missing functionality we have. Although as we will see by the end of this talk it is not as straightforward as having a cool idea and everybody cheering for you.

Spending Conditions: Scripts and Witnesses

An interesting thing about script. We use this word “script” which conjures up connotations of scripting languages like shell or Python or PHP or Node or whatever people use these days. A difference between Bitcoin Script and an ordinary scripting language is that in Bitcoin Script you are describing conditions under which a spend is valid. You aren’t executing a bunch of code. You literally are executing a bunch of code but morally what you are doing is demonstrating that some conditions exist that were sufficient to spend the coins and you have met those conditions. Scripts often specify a wide set of conditions. Say you have a 2-of-3 signature check then there are 3 different public keys. Any pair of those could be used to spend them. You may have a timelock with an emergency key. Maybe after a certain time has gone by, the original 3 keys have been lost, then there is an alternate key. You can do this but what hits the blockchain when you are spending coins is only one condition. You have the script that is describing a whole bunch of different things. Ultimately only one of them matters. Only one of them matters once the coins are spent. If they don’t get spent none of them matter. So it would be nice from a privacy/scalability perspective, it is nice I can bundle those up, there is usually a trade-off there. For the purposes of this talk privacy and scalability are going to come hand in hand. It would be ideal if we weren’t even revealing all these spending conditions. If at most one of them matters why are we publishing them all? Why are we making everybody download them? Why are we making everybody parse these? Why are we everybody check that they make sense and that they hash to the right thing etc.

So around 2011, 2012 on Bitcointalk I believe, which is where all Bitcoin ideas were invented. You can Google them and resurrect them as easy publication. There was an idea called MAST, Merklized Abstract Syntax Tree. I think now it is Merklized Alternate Script something or other. It is not quite MAST. The idea is that you take all these different spending conditions, you put them in what is called a Merkle tree. You take all the conditions, you hash them up, you take all the hashes, you bundle those together and hash them up. You get this cryptographic object that lets you cheaply reveal any one of the conditions or any subset of the conditions without needing to reveal all of them. This is smaller. What actually hits the chain is just a single 32 byte hash representing all the different conditions. When you use one of the conditions you have to reveal that condition and also a couple of hashes that give a cryptographic proof that the original hash committed to it. This idea has been floating around for quite a while. It has never been implemented. Why hasn’t it? For a couple of reasons that I am going to go into in more detail. One is that for something like MAST there is a wide range of design surface and because changes in Bitcoin are so far reaching and so difficult to do nobody wants to post something for Bitcoin and nobody wants to accept a proposal for Bitcoin that isn’t the best possible proposal that does what we are trying to do. For years we have had variations on different ways to do MAST. Different ways to hide script components. Questions about should we improve the script system at the same time as we are doing this? Should we change the output type and so on. Since 2012 we have had a number of different upgrade mechanisms appear. We have learnt a lot more about the difference between hard forks and soft forks and when hard forks are necessary and what they are appropriate for. We have learned new ways to soft fork in changes, especially changes to the script system, in ways that minimize disruption to nodes that haven’t updated. On all levels of this kind of change we have made a lot of progress over the last several years. In one sense it has been worthwhile. It is great that we didn’t try to deploy this in 2012 because what we did would have sucked. On the other hand it is 2020 and we still don’t have it. There is this trade-off that I’m going to talk about a bit more.

Spending Conditions: Keys Tricks

That is one of the two major ideas in Taproot. It is this thing MAST. You put all your spending conditions in a Merkle tree. You only have to reveal one. Nobody can see how many there are. Nobody can see what the other ones are, everything is great. The second part of Taproot is this family of things I am going to call key tricks. The standard Bitcoin script, address, whatever you want to describe it as, has a single key. You spend the coin by providing a single signature. Traditionally a public key belongs to one entity. It identifies that identity and it identifies the person who holds the private key, the person who is able to spend those coins. The idea is that there is one person with this private key. One person has complete and sole custody of the coins. It turns out there is a lot more you can do with keys, with single keys. A lot of this stuff is made much easier using Schnorr signatures versus ECDSA. I am not going to go into that but I am going to throw that out there. These are two different digital signature algorithms. They both use the same kind of keys but Schnorr signatures let you do some cool things with the keys in a much simpler way. The most important one that I have highlighted here is multisignatures. If you have several participants who all individually have a signing key, it is possible for them to combine all of their keys into one. What they do is they all choose some randomizers, they all multiply their key by some randomizer. This is a technical thing that prevents them from creating malicious keys that cancel out other participants. They add them together. I am using add in the sense of elliptic curves which is really like addition that most people are familiar with. But it behaves algebraically exactly like addition so we call it addition. You add these keys together, you get a single key out of this. Then what is cool is all these participants by cooperating are then able to produce a single signature for this single key and publish that to the blockchain. What the blockchain is going to see is one key and one signature. The same as if there was only one participant. The same as if it was an ordinary wallet that is not doing anything remarkable. But in fact behind the scenes there are multiple parties that all share custody of these coins and they all had to cooperate to move the coins. That is a cool thing. You can do variants of this. You can do threshold signatures. Instead of having 5 participants who all their combine their keys and then the 5 of them cooperate. You can have 5 participants combine their keys in such a way that any 3 of them might cooperate. There are 5 choose 3 different possibilities here and any of those 5 choose 3 possibilities of sets of signers are able to spend the coins. This requires a little bit more complicated interaction protocol between the individual participants but again what the blockchain sees is just one key, one signature. You can do more interesting things than thresholds. You can do arbitrary monotone functions, arbitrary different sets of signers can all be bundled together into one key which is pretty cool.

Another thing you can do with keys and signatures that we have learned is something called adaptor signatures. If you have two parties doing a 2-of-2 multisignature, they both have to cooperate to spend the coins, they can modify the multisigning protocol such that when the second party finishes the protocol, they complete the signature, by doing so they reveal a decryption key for some secret to the other party. A lot of what we use hash preimages and hashlocks for in Bitcoin is when you have two parties and you want one to have to reveal a secret to the other as a condition of taking their coins. We can bundle that into the signatures. I am not going to go into that but the keyword to lookup would probably be adaptor signatures or scriptless scripts. Adaptor signatures are the specific construction I am describing. This is the only equation that I am going to have in all these slides, last year I did 100 equations in a row in half a hour at the first talk of the Expo and I was told I scared people. This is a commitment equation.

P -> P + H(P,m)G

What is going on here? On the left hand side I have P for public key. I am going to modify my public key here. I am going to add the hash of the original public key and some arbitrary message m. I am going to multiply that by the generator of my elliptic curve group. What this multiplication does is converts this hash, which is a number, into a point which is a public key. This allows me to add them together. The effect of doing this transformation is that before I had a public key that I or some people knew the secret key to. Afterwards I have a different public key which the same set of people know the secret to. I have just offset it by this value which is a hash of public data. Anybody can compute it, I have just offset it. I haven’t changed the signing set at all. What I have done is turn the key from just a boring old key into a key that is actually a cryptographic commitment to this message m. I am using an arbitrary hash function H. If that hash is a cryptographic commitment, specifically if it is reasonable to model it as a random oracle then this construction also works as a hash. You can also model it is a random oracle and you can see that as long as I had a uniform distribution of hashes I am going to get a uniform distribution of points out of this. What is the point of this? The point of this is if I’m on the blockchain, I’m publishing a key and this key represents some sort of spending conditions. Now I can do one better, I not only have a key on the blockchain I have a commitment to some secret data. What is this good for? This is good for a couple of non-blockchain things like timestamping say. If I have some data, I want to prove that it existed at some point I can hide it inside of one of my public keys that I was going to put on the blockchain anyway. That goes into the Bitcoin blockchain that timestamps it. I have a whole bunch of proof of work on it. There are a certain number of blocks that were created after it. Everybody has a good idea of when every Bitcoin block was created, at least within a few minutes or a few hours. I have a cryptographic anchor for my message m to the blockchain. You can also use this to associate extra data to a transaction that the Bitcoin blockchain doesn’t care about.

For example at Blockstream we work on a project called Liquid which is a sidechain, it is a chain where you can move coins from the Bitcoin chain onto this other chain, Liquid. The mechanism of doing that is all the coins that are on the alternate chain, from Bitcoin’s perspective these are actually in the custody of this 11-of-15 quorum of who we call functionaries. To move coins onto the chain, you send them to the functionaries and then you go onto the sidechain and you write a special transaction saying “I locked up these Bitcoin, please give them to me on the sidechain.” The consensus rules of the sidechain know how to look at Bitcoin and verify that you did so. How do you say this is me? You are sending the coins to the functionaries, they are the same 15 people all the time. How do you identify that you were the one who locked up the coins when from Bitcoin’s perspective you gave them to the same people that everybody else did. You use this construction. You put some identifying thing here in this message m, throw that onto the Bitcoin blockchain. You then reveal m on the sidechain and the sidechain validators can verify this equation is satisfied. That is an example use of this.

Taproot Assumption

“If all interested parties agree, no other conditions matter”

The coolest use is going to be in Taproot. Let me throw out this maxim, the Taproot assumption. In most situations, most uses of Bitcoin script, you have this wide range of spending conditions that represent different possibilities for how your parties might interact, but ultimately you have a fixed set of parties that are known upfront. In a Lightning payment channel you have got the two participants in the channel. In an escrow type arrangement you have got the two parties in the escrow. In Liquid you have got the 15 functionaries who are all signing stuff. On a standard wallet you have got the one individual party. If everyone who has an interest in these coins agrees to move the coins they can just sign for the coins. As I mentioned two slides ago they can sign for the coins using a single key that represents all of their joint interests and do so interactively. The Taproot assumption is that in the common case, in the happy case of moving Bitcoin you only actually need a key and a signature. All this scripting stuff is there as a backstop for when things don’t go well or when you have weird requirements or weird assumptions. With that said we can get into where pay-to-contract comes in, where this commitment thing comes in. Here is where I describe what Taproot is.


We use MAST to hide our spending conditions in a giant Merkle tree. We get a single hash. We take that hash, we use our key commitment construction to commit to that hash inside of a public key which you put on the blockchain. Then we say the public key is how you spend the coins. What hits the chain is a single key, in the happy case with a single signature. Nobody even sees that any additional conditions exist. If you do reveal that they only see one of the conditions. In the typical case whether you are a normal wallet with a single key that is on a user’s hardware wallet or something, or if you are doing an escrow, or if you are doing a Lightning channel, or if you are doing a Liquid transfer, if you are doing a non-custodial trade, whatever you are doing, what hits the chain is one key, one signature. This is cheaper for everyone to validate than putting all the conditions explicitly on there. It is also much better for privacy because you are not revealing what the conditions are, you aren’t revealing that there were any special conditions. You are not revealing how many participants were involved, how many people have an interest and what that interest looks like. You are not revealing any of that. That’s Taproot. There’s a whole bunch of detailed design stuff that I am not going to go into here. At a high level that’s the idea.

Designing for Bitcoin

In the next five minutes let me talk about some of the design considerations that went into this. The different ways that we had to think about Taproot.

Is Bitcoin Dead?

Before I do that let me quickly talk about Bitcoin development. I know a lot of people here are MIT students or students from other universities. There is a perception that there is a lot of really cool stuff happening in the cryptocurrency world. There are all these new things being developed, all these new technologies being deployed. Meanwhile Bitcoin is the dinosaur in the room. It never really changes and it doesn’t have any of the cool stuff. It doesn’t have the cool scripting language, it doesn’t have all the cool privacy tech. It doesn’t have DAGs, all this cool stuff. There is this idea that Bitcoin maybe hasn’t really changed in the last several years. We don’t have new features and new press releases saying “Here is a cool thing you can do on Bitcoin that you couldn’t do before.” On some level everything you can do in Bitcoin in 2020 was technically possible in 2009. Although very very difficult and very inefficient for many reasons. The reason for this perception is that deploying new things on Bitcoin is very slow. If you have a proposal you need to write it up, you need to have a detailed description of the proposal. You need to have code that is written. You need to have a fair bit of buy-in from the developer community. That is to just have a proposal, to have something that somebody is willing to give a BIP number to. A BIP number means almost nothing. Then you need to go through probably years of review, you need to get input from various stakeholders in the ecosystem, you need to go through all this rigor and rigmarole. It is a very long process and it can feel frustrating because there are a lot of other projects out there where you have a cool idea, you show up on the IRC channel and they are like “Wow somebody is interested in our stuff. We will deploy your thing of course.” Then you get stuff out there. You see various projects that are having hard forks every six months or something, deploying cool new stuff that is very experimental and very bold. That is super exciting but Bitcoin can’t do that. The requirements in Bitcoin are much higher. In particular Bitcoin is by far the most scalable cryptocurrency that is deployed and it is probably not scalable enough for serious worldwide usage. We are really hesitant to do anything that is going to slow down validation. Even to do anything that doesn’t speed up validation. That is maybe the most pressing concern. Others would argue that privacy is the most pressing concern. That is also a very valid viewpoint. Unfortunately improving privacy often comes with very difficult trade-offs that Bitcoin is unable to make in terms of weird new crypto assumptions or speed or size. Despite the difficulty in deploying things the pace of research in Bitcoin is incredibly fast. I hinted at all of these things we can do with keys and signatures. Over the last two years we have seen this explosion of different cool things you can do just with keys and signatures. There is an irony, it is so slow to deploy stuff on Bitcoin. What do we have? We have keys, what can we do with keys? But we have actually done a tremendous amount with keys, far more than anybody even in the academic cryptography space would’ve thought. Let’s do cryptography but the constraint is you are only allowed to output a key and a signature at the end. First of all they would say “That is the most ridiculous thing I have ever heard.” I actually did a talk at NIST once and I got belly laughs from people. They thought it was hilarious that there was this community of Bitcoin people who had tied their hands behind their backs in such a dramatic way. A result of all this is that there is a tremendous amount of research that is developing really cool stuff. Really innovative things that wind up having better scalability and better privacy than those things that we would’ve deployed in the standard way where we are allowed to have new cryptographic assumptions, we are allowed to use as much space as we want or we are allowed to spend quite a bit of time verifying stuff.

The Unbearable Heaviness of Protocol Changes

As I mentioned, I am going to rush through these two slides, there is a lot of difficulty even if you have a proposal that checks all these boxes you have got to get through a whole bunch of hoops. This change has to be accepted by the entire community which includes very many people. It includes miners, the protocol developers, the wallet developers who often have opposing goals, HSM developers who are in their own little world where they have no memory, no space and no state and they want the protocol to be set. We have retail users who just want their stuff to work and who often want bad things to not happen even when the cryptography guarantees that bad things will happen to them. You have institutional users who care even more about bad things not happening. Exchanges, custodians etc. All of these people have some interest in the system. All of these categories represent people who have a large economic stake in the system. If any change makes their lives meaningfully worse without giving them tremendous benefit they are going to complain and you are not going to get your proposal anywhere. You are going to have endless fights on the development mailing list. Just proposing an upgrade at all is making people’s lives worse because now they have to read stuff and you are going to have fights about that.

Bitcoin, I checked this morning, has a market capitalization of about 170 billion dollars. This is not flash in the pan money, it has been over 100 billion dollars for several years now. When we deploy changes to Bitcoin on a worldwide consensus system these changes can’t be undone. If we screw up the soundness and it forks into a million different things. There is no more agreement on the state of the chain, probably that is game over. If people lose their money, if coins can get stolen it is just game over. It may even be game over for the whole cryptocurrency space. That would be such a tremendous loss of faith in this technology. Remember in the eyes of the wider public, as slow as Bitcoin is to us, it is really fast, reckless, all this crazy cypherpunk stuff, going into a computer system that has nobody in charge of it that is supposed to guarantee everybody’s life savings. It is nuts. If we screw it up we screw it up, game over. We all find new jobs I guess. Maybe go on the speaking circuit apologizing. That is the heaviness of protocol changes.


A couple of quick words about cryptography. In the first half of the talk I was talking about all these cool things we can do with just keys, just signatures. Isn’t this great? No additional resources on the chain. That is not quite true. You would think adding these new features would involve some increase of resources at least for some users. But in fact we have been able to keep this to a couple of bytes here and there. In certain really specific scenarios somebody has to reveal more hashes than they otherwise would. We have been spoilt with the magic of cryptography over the last several years. We have been able by grinding on research to find all these cool new scalability and privacy improvements that have no trade-offs other than deployment complexity and so forth. Cryptography can’t do everything, we think. There aren’t really any hard limits on what cryptography can do that necessarily prevent us from just doing everything in an arbitrarily small amount of space. But it is an ongoing research project. Every new thing is something that takes many years of research to come up with. When we are making deployments, I said if we make anyone’s lives worse then it is not going to go through. This includes wasting a couple of bytes. For example on Taproot one technical thing I am going to go into is we had public keys that took 33 bytes to represent. 32 bytes plus one extra bit which represents a choice of two different points that have the same x coordinate. We found a way to drop that extra bit, we had to add some complexity. There was an argument about how we wanted to drop that extra bit and what the meaning of the bit would have been. Would it be the evenness or oddness of the number we alighted, would it be whether it was quadratic residue? Would it be what part of the range of possible values it lives in, stuff like this. That is the kind of stuff that we spent quite a while grinding on even though it is not very exciting. It is certainly not some cool new flash loan technology or whatever that various other projects are deploying. This is stuff that is important for getting something through on a worldwide system where everybody is a stakeholder and no one wants to spend money on extra bytes.

Political Things

Finally a few general words about politics. I deliberately ran out of time here so I wouldn’t have to linger on this slide. I have said most of this. Usually when we think about Bitcoin politics, those of us who have been around for a little while think about the SegWit debacle where we had this UASF thing going on. We had miners doing secret AsicBoost and we had misalignment of incentives between users, developers and miners. There was this fork, Bitcoin Cash, all this grandstanding. People saying “We are going to create a fork such that we have no replay protection so that if you don’t give us what we want we will cause all this money loss.” That was pretty dramatic but that is not really what Bitcoin politics is like generally. Generally Bitcoin politics are the things that I have been talking about. You have a whole wide set of participants who are generally afraid of change and complexity for very good reason by the way. We have seen a lot of technology failures on other projects deploying things too rapidly. We have a lot of people who feel that Bitcoin is increasingly onerous to validate. The blockchain is getting too large, it is already too much of a verification burden. That’s is what we should be doing, reducing that somehow. We have people who think privacy is the most important thing. Again with good reason. Bitcoin’s privacy story is absolutely horrible. We have an aversion to reading stuff, as people in this room probably are aware, when you propose things for Bitcoin it can be hard to get people to read your emails. Especially if you have some cool new crypto that requires a lot of cognitive load for people to read and for people to deploy. It can be difficult to compete for people’s attention. Even once you succeed on that there is a long process. There is going to be a lot of bikeshedding on various trivial features of your proposal that you have to be polite with and try to come to a conclusion. On the opposite end with bikeshedding you are going to get demands for proof, demands that you prove your idea and you deploy it in a solid way. That can take quite a bit of time and energy.


Q - This would work for any blockchain or ledger? Grin etc It would work for all of them?

A - Absolutely. But in Bitcoin there is a much more extreme aversion to experimental technology. All the blockchains you mentioned were deployed around some new technology that they wanted to prove. By nature these are more willing to accept new ideas or ideas that maybe have different trade-offs in terms of algorithmic complexity or cryptographic assumptions or something like that. But any blockchain that expects to survive and expects to continue to work for its users, all these considerations apply.