# Privacy Preserving Multi Hop Locks

Speakers: Pedro Moreno-Sanchez

*Transcript By: Bryan Bishop*

Tags: Research, Adaptor signatures

Category: Conference

Privacy preserving multi-hop locks for blockchain scalability and interoperability

https://twitter.com/kanzure/status/1091026195032924160

paper: https://eprint.iacr.org/2018/472.pdf

http://diyhpl.us/wiki/transcripts/scalingbitcoin/tokyo-2018/multi-hop-locks/

## Introduction

This is joint work with my collaborators. Permissionless blockchains have some issues. The permissionless nature leads to the transaction rate that they have. This limits widespread adoption of blockchain technology like bitcoin or ethereum. Scalability approaches can be roughly grouped into two groups, one is on-chain layer 1 solutions. The other group is off-chain layer 2, which is the focus of this talk today.

## Payment channels

The technique most widely deployed for layer 2 today is called payment channels. Just to make sure everyone understands, there are two users Alice and Bob. Bob has some books. Alice wants to buy the books with bitcoin. Alice could pay for each book with an on-chain transaction but this will add more load to the blockchain and she will have to wait for more time. So instead, she is going to use a payment channel.

A payment channel requires a commitment transaction. It’s a deposit account shared by both Alice and Bob. Just to make sure, after some time, Alice can get her money back even if Bob disappears. Using this commitment structure, it’s possible to rebalance the amounts in the channel between the two parties. These transactions can occur off-chain and then be committed to the chain at the end.

This technique is nice, but it only works for two users.

## Payment channel networks

It would be nice to have a system where everyone can make payments to everyone. So the first idea is to create channels between every users in the network. This is impractical because you need to lock coins in each channel. Some people might not have enough coins to do that. Instead, users can open up a few channels with their friends and then rely on the fact that there might be other channels open that connect them to the receiver in a large graph. In effect, you rely on other channels to reach the intended receiver.

## Current payment channel networks

This has been deployed already in practice: lnd, c-lightning, eclair, raiden network on ethereum, BOLT on zcash, and eventually every blockchain might need a layer 2 scalability solution.

## This talk

The focus of this talk is mainly on three points:

We formally describe the security and privacy notions we need for a payment channel network.

We analyze current payment channel networks and show security and privacy attacks.

Then we provide cryptographic constructions with formal security and privacy guarantees.

## Security in payment channel networks

We define security here as “balance security”- honest users do not lose coins in an off-chain payment. There is a path of multiple users between the sender and receiver. The intermediary node has a balance, the number of coins he has in the payment channel. The payment channel network if it has security should ensure that after a payment goes through Bob then he will not have less coins than he had before. The probability of this occurring should be extremely small.

There’s a concept called a hash-time lock contract (HTLC) to enforce this. Payment is conditioned on revealing the pre-image of a hash. This looks like HTLC(Alice, Bob, 1, y, t). There will be a script that says if Bob comes up with some value such that the hash of something is equal to something else, then Bob gets his coins.

## Lightning network

Multiple “chained” HTLCs allow multi-hop payments in the presence of malicious intermedaries. There’s a path between sender and receiver, and it requires multiple hops. Alice creates a conditional payment to Bob, and Bob creates a payment to the next intermediary that is also conditional. Also, there are fees charged by intermediaries for providing the routing service and payment network services.

## A novel wormhole attack

The idea is to exclude intermediate honest users from successful completion. The consequence is that an adversary can steal fees from honest users. He would be able to steal the routing fees from the honest user. Intermediaries in the path can collude and prevent honest users from successful completion of the path. The same conditoin along the path enables this attack. More intermedaries, more benefits. This is important because fees are the basis for the payment channel networks. Since he knows the same condition has been used in the whole path, he can use the same opening condition to claim money from Alice. In the end, the adversary gains coins.

The main issue why this attack is possible in current payment channel networks is that the same condition is at each hop along the path. The intermediary (Bob) believes that the payment is unsuccessful and no payment was done. He cannot pinpoint the adversary as somebody that did something wrong. The more intermediaries, the more the adversary benefits.

## Privacy

Before we talk about privacy, let’s agree on a notion of privacy. Here we define it in terms of relationship anonymity, which means that the adversary should not be able to tell who is paying to whom in a payment channel network. In a more practical definition, suppose there’s two senders and two receivers. The adversary should not be able to tell which sender is paying to which receiver. The probability that his guess is correct should be really close to the probability that the adversary is wrong. The only thing that he can do in such a path or payment is guess, he doesn’t get any additional information from the payment itself.

Once we have agreed what privacy means, let’s look at how privacy is implemented in current payment channel networks. Again, we are using the same example of two senders and two receivers. If the adversary is in the same path at multiple hops, then because the same condition is used in the complete path, then the adversary can learn information.

## Other practical considerations

WE also looked at other issues such as scalability. Two keys are needed to define the deposit, and there are payment conditions and signatures that are required. This contributes to a scalability problem.

There are also privacy issues: users share a channel get revealed. It can be revealed that those two users were doing business together.

There is also interoperability: support for specific hash functions is required. If you want to use that network, then you need to use the hash function they have implemented in their system.

## Summary of current payment channel networks

Payment channel networks have definitely improved scalability in the current networks. However, we see that in security and privacy there are big problems.

## What can we do with the signatures?

We looked at the transactions and we saw that in many cases, the signatures are used to authorize transactions. We thought, could we use signatures for something more than authorizing transactions?

## 2-party ECDSA

There was a paper in 2017 called 2-party ECDSA signing https://eprint.iacr.org/2017/552.pdf - the idea is that it is possible to jointly compute a signature on a transaction. It requires the knowledge of both secret keys from both participants. It can be publicly verified using a public key which is the combined public key of both of them.

So this could be used in payment channel networks. Instead of using two keys, we can use only a single key. These bytes are saved both in open channel operations and also during off-chain payments. But remember, for multi-hop payments we need to embed conditions or constraints. What if we could encode the conditions itself into the signature or the public key?

## Scriptless scripts

For that, there is a technique called scriptless scripts proposed by Andrew Poelstra. It’s possible to encode cryptographic conditions into the Schnorr signatures. The technique he proposed requires Schnorr signatures. They have done excellent work on how to expand this to more functionality, but unfortunately Schnorr signatures are not used in bitcoin, instead we use ECDSA. So we require a similar technique for encoding conditions inside of ECDSA signatures.

In our work, we first formally defined the work of Poelstra, and then we proposed a scriptless scripts version of ECDSA. What I wanted to point out is that this was an open problem for a while. The main challenge to make this work is that the signature structure… the randomness plus the secret key by the message. You could do linear combination of two signatures. But in ECDSA, the structure of a signature is a bit more complex and it requires the inverse of numbers and some other things, and it’s not a nice linear combination. It’s a complex combination of two signatures. It requires inverse, x coordinate of a point and a multiplicative shares of the secret key. If you’re interested in the detail, we have the full protocol sketch in the paper. I don’t have time to tell you about that, but I’ll give you a brief overview.

So you have two users Alice and Bob that want to make a payment under the condition that the receiver can make a key, such that Bob can only finish the half-signature when he solves the problem. If Bob actually manages to do that and solve the condition and create a finalized signature, Alice should be able to look at this signature and extract or learn the secret key from that.

The first thing we do is we create the joined public key, and create a combination of the randomness which combines randomness from Alice, randomness from Bob, and the condition itself. This ensures that Alice must use her secret key, Bob must use his secret key, but also they must use … secret key… Once they have done that, Alice gives 1/3rd of the signature to Bob, and Bob gives 1/3rd of the signature to Alice, and at the end if they learn the other third then they can complete the signature. Either party can learn the secret key. She can release the payment by creating the whole signature.

## ECDSA-based payment channel network

Multiple “chained” ECDSA conditional payments allow multi-hop payments in the presence of malicious intermediaries. Alice gives to Bob the combined public key plus the secret key for the other one and another one. The receiver gives a condition and the opening of that condition, the secret key associated to that public key. If she is the receiver then she can open the payment and see everything is satisfied. Bob can lock the inocming payment channel in the combined public key, and the outgoing one in the other public key. He knows that once the receiver reveals something, then this information is the opening information for the combined public key. So he knows he can take information from the receiver taking the payment and be able to open up the other lock. The release part of the protocol is similar.

These locks are randomized conditions, which enforces the security and privacy notions that we were looking for.

These ECDSA-based locks can be extended to n hops. It solves the security problem (wormhole attack) and the privacy issues I discussed earlier. This technique improves interoperability, because it only requires ECDSA. We show in the paper that it is possible to combine ECDSA payment channels with Schnorr payment channels, and you could still all be in the same multi-hop network. This is based on ECDSA, so it’s compatible with bitcoin.

implementation- https://github.com/cfromknecht/tpec