Using the Chain for what Chains are Good For

Andrew Poelstra (andytoshi)

I am Andrew Poelstra, a cryptographer at Blockstream. I am going to talk about scriptless scripts. But this is a specific example of a more general theme, which is using the blockchain as a trust anchor or commitment layer for smart contracts whose real contents don't really hit the blockchain. I'll elaborate on what I mean by that, and I'll show what the benefits are for that.

To give some context, in Bitcoin script, the scripting language which is used to encode smart contracts which go on to the blockchain and eeryone verifies the chain and to download and execute all of this contract code. Everyone validates the chain. Everyone that wants to trustlessly learn the stat eof the system has to download and parse and validate. They can't compress or aggregate the data. They can't make it smaller due to kolmogorov complexity. The contractors doing this, before they publish, to be ensured that it doesn't get reverted, the transaction must first be confirmed. This is a poisson process. Once your transaction lands in a block, you need additional assurances. You never have perfect finality, too.

In addition to this, the contracts encoded in script have rules that everyone needs to agree on. If there's any disagreement in the system or network about which scripts are valid or invalid, would cause a disagreement on the history of the chain and that's a consensus failure, and as a result everyone needs to agree on the rules beforehand. So adding more functionality is often a painful process, as we have learned recently.

Additionally, I also care about the details of the script. The details have to be there and stay forever. If people are doing a complex transaction amongst themselves, tmaybe they don't want that data to be visible outside of their group. But once your contract is published, everyone sees it, it has to be kept forever because future validators need to be able to see it. And related to this, when transactions are collected into blocks, miners can choose whatever transactions they want and they are incentivized to go with the highest fee but this incentive is only within the system. There are external incentives though, and the real world can interact with the mining process here. Miners that can see contract details become a target to government and external systems and they might not want that liability. We don't want them to be able to see that data, because it's a censorship risk, and it's a liability to the miners which they don't want to have.

All of these contracts executed by explicitly published code are really only usin the blockchain for one thing- to get an immutable ordering of what order tha ttransactions happen in. All that they really care about is that the transaction is not reversed and not double spent. This is the core competency of bitcoin blockchain. This is what I mean by my talk's title. This is what needs to go into the blockchian. If we can do that in principle, we hsould be able to aoid putting anything else in the blockchain into there. It should just be inputs and outputs. The exact conditions under which this can happen can bwe reduced to a ery small amount of data that doesn't reeal thwat the commitments are.

There's a distinction between alidation and execution. We see this in two places. In general in computer science, when you talk about turing machines s turing deciders, there's a post theorem that shows that it's strictly easier to alidate the execution than it is to.... because you can proide a witness which shows it. Instead of executing the script. In crypto, we talk about validation vs execution. In computer science, it's about how expressive it's required. Verification of something can be done in zero knowledge where the helper data is not revealed to everyone, but through the magic of cryptography everyone can verify that the extra data existed and it was correct.

In addition to execution vs verifiability distinction, there's verifiability vs public verifiyability. The blockchain verifiers care about the state of the system like where the coins are, how many coins there are, what they are assigned to and so on. When they see a transaction, they want to know that the transaction is authorized and that they agree. But they don't care too much what it truly means. When you're transacting, you care about faithful execution and the rules you want to enforce. But everybody else doesn't care- only that the rules were followed and that whoever owned the money before was somehow okay with it moving. This is much more nebulous thing than what the transactor probably cares about.

There's kind of a general way to do contracting, which Adam Gibson talked about in a recent or upcoming blog post where you can imagine instead of doing some complex ethereum contract or series of bitcoin scripts... suppose you only care about money moving only under external conditions. You can moe your coins to a ultisig output. Eeryone has to sign off on it. When you set itup, you do a locktime refund transaction and so on with a timeout. Under some external conditions, each signer cares about, checks the conditions and only then do they sign off. What the blockchain alidators check is that the signatures are present. They don't care about the external conditions are. They odn't need to download a description of those conditions or anything like that.

Suppose, though, that the conditions that the signers want to enforce are not just external things about the world that they can look at. Suppose they want to enforce conditions on each other, the classic example is an atomic exchange between blockchains, like giing money to someone in exchange for other altcoins. And bitoin and tehereun ahae dierent lofefaidf. And each one on deach chains. And if I sign to gie my coins away, my ice ers,a we hae to sign simultaneously. We hae to enforce onditions on each other. I will talk on the next slide about how todo this.

You can do this in bitcoin script or ehteruem or whateer, ... in the classic way where in order to take the coins you hae to reeal a hash preimage. In both blockchain, reealing this hash preimage reelation is a requirement. One person knows the hash preimage, to do this they reeal hash preimage which they do by creating a bitcoin script that says these coins must not moe until someone reeals the hash preimage to take the coins. At that point, the other person can read the preimage off of the public blockchain and take their coins. And thus atomicity has been achieed.

This isn't good: it links the two transactions becaus eyou see the same hash preimage. And it also forces the erifiers to download the hash, the preimage, and check them foreer. The erifiers don't really care about that. Only the two transactors only care about the hash preimage, and only then for a limited time. But somehow the data is still there foreer?

I hae been working on a way to do scripts in an inisible off-chain way, using witness data like a hash preimage is hidden in the signatures themseles. Validators will always have to check signatures themselves. Validators are already checking this. My program here is, how much extra validation can you oerload these signatures with? So only the people producing the signatures know this other stuff. But the validators won't know.

I am taking digital signatures and adding some extra semantics to them. It turns out that you can do a lot like this. This historically came from the mimblewimble project that does not have support for scripts. There was an ope nquestion when it appeared: how do we do any contracting, atomic exchanges, lightning? One answer turned out to be scriptless scripts, and that's where it came from, but it turns out tha tit's applicable to bitcoin. Most of what I am doing requires that we have support for schnorr signatures in bitcoin, which would require a new opcode. It doesn't add any new semantics to the system, it just creates an alternative to the ECDSA signature algorithm that people can use if they want to.

Benedikt talked about schnorr signatures yesterday. There's one equation here, but it's jus ta plus sign, so it's okay. In schnorr signatures, you can create multisig with two parties or more, that look... same.. single signatures. They do this by interactively producing a signautre on a joint signing key. Each one has a signing key. They add them together and they are able to make a signature. A cool feature here is that when they are doing this interaction they first agree on the first half of the signature which is something like an ephemeral temporary public key (a nonce). And then they produce the real signature. I am going to stick a bunch of extra data into those steps. It never hits the chian. Once it hits the chain, it's just a signature. But we can do some cool things in this space between signers.

I am going to use an "adaptor signature" where the two components of these schnorr signatures can be modified in such a way that we can add some random number t such that you can get a real signature knowing the secret value t and knowing the value secret t you can get a real signature. Knowledge of this value t becomes a key to producing this signature. The way this is done is using this thing called a valid signature. Someone can verify the adaptor signature. There's a little t value and a big T value.

Once Bob signs, Alice has some secret information that she can use to get her coins.

Adaptor signatures can be used instead of hash preimages. These discrete log challenges, have a bunch of extra structure. One is that you can make them work across elliptic curves with some extra cryptography that I will publish in the next few months. So even between Monero using ed25519 and then bitcoin with secp256k1. The adaptor signatures are undetectable and they are deniable. What winds up hitting the chian are just these normal looking schnorr signatures, and this off-chain interaction where Bob secretly re-blinded these and passed them to Alice is undetectable and deniable. Anyone can take these two signatures after the fact on any blockchain, add them and make them look like an adaptor signature or whateer; there's no eidence that the original stuff happened at all. This is good for privacy and fungibility. Coins that are used for various protocols like this are indistinguishable from coins used for normal p2p protocols.

An additional cool feature of scriptless scripts is that these adaptor signatures are re-blindable. You can chain not just two transactions, not just two transactions made atomic. You can make arbitrary chains of transactions atomic. I can make all the hops happen atomically. This is what lightning is based on. You can do this knowing that there's no risk of coins being stolen because it's all happening atomically. There's a privacy issue with using hash preimages ( a standard way to do this ), where each party reeals a hash preimage and then the other parties can observe this. But eahc hop could have a custom challenge, and translate it into a new challenge. The participants in the hops are unable to tell without complete collusion that they are part of the same path even given the extra data. Nothing that hits the chain, no hashes that they can look at, to identify it. Even given the secret data they are passing amongst each other-- even then each hop in the path involves uniformly random data that is uncorrelated with every other hop in that path or any other path. So that's great thing for privacy on lightning.

Q&A

A: You can do threshold signature tricks and that is completely compatible with this. You can have each party revealing different things to differnet people and they can have different weird structure ot their adaptor signatures.

Q: How do you reeal the alue?

A: Alice ... alng with a alid signature with little t. Once you know s + t, and if you learn t or s, you can get the other one.

Q: So the signature will...

A: Exactly. There's an additional thing gien. That's the adaptor signature, is s + t.

Q: ... linkability between the two... like atomic swaps.

A: No. The reason is that, after the signature is on the chain, there's little s hitting the chain. Anyone can make up some t value and T value. Add little t to the signature and... and pretend it was some other r value. You can do this with any t value, it's independent, there's nothing tying this particular t value.

Q: Storage and transactions implication of this approach?

A: Using schnorr multisigs, there are multiple signatures being combined into one. A signature on any transaction input could be reduced from 128 bytes to 64 byte signature. In addition to that, using something like an atomic swap, and something like a hash preimage, thats another 64 bytes.. In this atomic swap example, rathe rthan having about 200 bytes of data which is multisig plus a hash and a preimage, that's collapsed into one signature which is only 64 bytes. And on top of that there's an additional topic called aggregate signatures which can reduce from 64 bytes to 32 bytes. The rest of the transaction is the same, the shape of the transaction is the same.

Q: This feels related to Tadge's work?

A: I would love if Tadge would describe his work as a scriptless script so that I can claim to have a wide umbrella. I described adaptor signatures-- you could do other stuff like pay to contract, sign to contract, discreet log contracts, and another thing I hae been working on that might be public in the next few months. I wanted to gie an example of what hiding hte contracts offers to the chain. I wanted to motiate the paradigm.