# Solving Data Availability Attacks Using Coded Merkle Trees

*Transcript By: Bryan Bishop*

Category: Conference

Coded Merkle Tree: Solving Data Availability Attacks in Blockchains

Sreeram Kannan

https://eprint.iacr.org/2019/1139.pdf

https://twitter.com/kanzure/status/1230984827651772416

# Introduction

I am going to talk about blockchain sharding via data availability. Good evening everybody. I am Sreeram Kannan. This talk is going to be on how to scale blockchains using data availability proofs. The work in this talk is done in collaboration with my colleagues including Fisher Yu, Songza Li, David Tse, Vivek Bagaria, Salman Avestimehr, etc.

# Sharding proposals

If you look at the state of sharding today, there have been many academic works:

- RapidChain: Saling blockchain via full sharding
- OmniLedger
- A secure sharding protocol for open blockchains

There are also many blockchains built on top of sharding. It’s critical for us to understand how these things work. There are many proposals, but there is one common thing between all of them. In all of these proposals, the way you scale a blockchain is first by subdividing your ledger into multiple groups.

# Sharding key idea: node-to-shard

There are subledgers maintained by distinct subgroups. To decide who maintains those shards is the role of a node-to-shard allocation algorithm. How do you know which nodes should run which shards? All the existing proposals have a verifiable allocation algorithm that takes nodes and sorts them into different shards, randomly. The randomness is cryptographically provable so that you cannot cheat.

This sorting is required because you do not let the adversary congregate into any one shard. The adversary power gets sieved equally into different shards. This being the key idea in many of the existing proposals, the main result of these sharding works is the following.

# Performance

You can get very high throughput. The value k is the number of shards that you divide your ledger into. Yhe throughput is O(k). The computation is as though you are only maintaining one subledger so that’s O(1). The storage and communication are both O(log k). The claim is that you can tolerate up to 50% adversary power using these kinds of methods.

# Adaptive adversary problem

If this is the case, then it seems to be near optimal on all these metrics. Why are we here? The problem with all existing sharding approaches and the reason why you have 10 different approaches to sharding is the adaptive adversary problem.

When you sieve the nodes through the cryptographic allocator. The nodes will get allocated to various shards and then the adversary will decide which shard to takeover. The adversary you can bribe once you know you want to manipulate a shard, you just bribe the few nodes which have been allocated to that shard.

What this does is change the equation significantly. Why? Because now the tolerable adversarial power in each shard is not 50%, it’s 1/(2k) because the adversary can congregate on the shard. This is the adaptive adversary model. Okay?

# Fraud proofs and verifiable computation

Many of these different projects have ideas about how to deal with adaptive adversaries. Many of them either rely on fraud proofs- that you can prove to the others that somehow the transactions were invalid, or by using verifiable computing which is providing proofs a priori that your computations were done correctly. However, no fraud proofs can guarantee that there is no censoring. In fact, Vitalik talked about it yesterday in his talk.

# Trifecta sharding

I am going to introduce a simple sharding proposal. Here’s the idea. You take all the nodes and split them into different shards. I am going to propose something radical: let the nodes choose which shards to live in. I am not going to boss around and choose who goes where, it’s a free world after all. What happens? Each of the shards mine blocks. All the nodes together mine a common shard. That’s in blue on the right. Blue nodes mined by everybody. It’s very secure, the blue chain. Okay, so. What is going on now? The blocks come in from all these shards, they get referred– … the hash of block number a1. So the next block, the next blue block refers to b1 and c1. Each block refers to some subset of shard blocks. They get ordered into these different shards. This seems very similar to most protocols out there.

What is the difference to the other protocols? Here what we are going to assume is that we’re not going to let the main nodes claim whether the blocks were valid or not. We don’t worry about validity. The main chain is just providing an order on a shard chain.

Why is this interesting? It’s very simple, okay, and similar to other things other people have done. Why is this interesting? It’s interesting because if you want to manipulate the order on a given shard, you have to go and manipulate the order on the main chain.

This improves your security from 1/(2k) to 50% adversary required. Are we done? Not so fast. Let’s understand what’s going on in the main chain. How do we obtain shard C? I want to know what the subledger is on shard C. So I go and read out what are all the pointers to shard C in the main chain. So you see c1, c3, etc. Now I construct the shard c ledger, by thinking of this as an ordered list. You read the ledger up to down on this sharder. Note that since we did not guarantee transaction validity, okay, we did not guarantee transaction validity so there might be double spends and other invalid transactions in this shard. However, it is not an issue because anyone executing shard c will all reject double spends which come one below the other.

# Data unavailability attack

However, there is a more insidious problem, a very central problem to this architecture. So you go to the main chain and find the sequence of blocks for shard c, and you go around to all the nodes in shard c and you ask them could you please give us these blocks. What if a certain block is nowhere to be found? Nothing in this architecture currently prevents this attack.

We need an oracle that is going to tell us when a block is available. Suppose we had such an oracle available. How would we run the blockchain with that? Say you want to include a hash commitment into the blue chain, you better ask the oracle before including that link. Very simple idea. You can ask the oracle, and he will tell you whether the block is available or not. You’re going to ask the oracle and make sure this never happens.

# Data availability oracle

This raises the data availability problem and the data availability oracle. This problem was pointed out yesterday in another talk. We’re going to deep dive into this problem. I am going to abstract this problem from all the sharding context. Just think about the nodes in the shard that have a block. You can think of any node in the main chain that doesn’t want to bother downloading the entire block, but somehow it needs to figure out if the block is available or not.

When you get a block in the shard, you’re just going to forward a commitment to the main chain. Somehow, the main chain should be able to use this commitment and some interactive game to figure out whether the block is actually available.

# Random sampling

Here’s the first idea for how to solve this problem. The idea is since I have a commitment to the block, I can ask the node ot send me the commitment. I can ask random questions about the block to that committing node. For example, if this node– if a node sends you a certain commitment then you go and query that node- can you send me chunk number n? Think of a block as being comprised of many chunks, and you query the node and it sends you a chunk from the block.

So you just randomly sample the block. If you got all the queries, then maybe you assume the block is available. But there’s a problem with this: if the node was malicious, what is it going to do? It’s not going to hide a lot of chunks. If it hides a lot of chunks, then you’re going to detect it. It’s going to hide a very small fraction of chunks, maybe just one chunk, which makes the block unavailable because when you try to parse the ledger and you’re going to have some ledger portions unavailable and you won’t be able to parse the ledger.

If the adversary hides only one chunk, then you’re unable to verify quickly whether the data is fully available or not. So that’s the problem now. The problem is that the adversary can get away with hiding a very small number of chunks.

# Improving sampling efficiency with erasure codes

musalbas et al proposed erasure codes. You encode the block using an erasure code. The propery of an erasure code is that even if some fraction of the chunks are unavailable, you will be able to download the available chunks and get the whole data out of that. The only way that the adversary can hide the chunk, then they must hide half the total data. If they hide less than half the data, the user would be able to reconstruct the whole block.

A node can now easily check that half the data is available. The adversary has to respond. The probability that you will find a missing chunk is 1/2. So if we sample 10 chunks, you have a high probability that you detect a hidden or invalid chunk. A small number of checks are sufficient in this protocol.

# Role of other full nodes

Whenever you have adversarial space, you have to be careful. As you open the algorithmic space, your adversarial space gets enlarged. So now the adversary can do not only hiding, but also something else. So what can it do? The adversary can create an ill-formed block. What does that mean? A good block will have the following property: it should be encoded in a certain way. But what if the adversary committed to a block which is not encoded correctly? It just puts in some random junk instead and commits to the random junk and then commits to that block. The block is ill-formed, ill-coded, okay. The adversary can hide that ill-coded portion. Now if a regular node tries to query, he finds one chunk is unavailable, he is going to assume by sampling a couple of chunks that maybe the whole block is available.

Here is where other nodes become critical. What is the role of the other nodes? Remember this node belonged to a shard, but there are other nodes in the shard too. These nodes are monitoring all the chunks that are being delivered by this block producer, and they are going to do erasure decoding to retrieve the unknown chunk. In this example, the chunk that was unknown was this ill-formed chunk and it does erasure decoding and tries to interpolate and it gets a certain answer.

However, that answer does not match the commitment to the block. So to summarize, the adversary made an ill-formed block, the regular node assumed that the block is available because the randomly sampled chunks were available, and the other nodes which are in the network are observing this process and decoding the data and found out that there—- this is a proof that the data was ill-formed. You have all the other chunks and they have commitments… if you try to extrapolate from there, what you see is that they don’t match the commitment.

We have converted a temporally-fluctuating data availability problem, however ill-coding fraud is not temporally fluctuating it is a provable fault. The other node can send a proof that the block was ill-informed. You converted an unstable temporally-fluctuating problem into a stable, provable problem. Okay.

# Problem abstraction and metrics

Now it seems we have taken this approach, and that solves the entire problem. You have a node, the lite node has a commitment… What happens if you just use a regular erasure code? The first metric of interest is the header or commitment size. How big is the commitment? The second metric of interest is the sampling size: how much do I need to sample to be sure that the data is available? Other nodes have to decode this block, so they have a decoding cost imposed on them. Finally, these other nodes are sending a fraud proof and this fraud proof if it is really big, this leads to a denial-of-service attack. So there’s at least four dimensions of interest.

# Existing results

We have header size, sampling cost, coding-fraud proof size, and decoding complexity. Say b is the size of the block. State of the art basically reduces… just Reed-Solomon codes.. but in the paper by musalbas et al, they proposed a new construction based on Reed-Solomon however the header sized increased. It’s not a constant sized commitment. The coding-fraud proof size is not constant but square root sized. The main question is, is it possible to improve these?

# Coded merkle trees

Coded merkle trees give you optimal header size, sampling cost, coding-fraud proof size, and decoding complexity. That’s what we show in our work. I am going to introduce the algorithm of the coded merkle tree.

Most of you will be familiar with the merkle tree. Here is what we’re going to do. We take the block, split it into chunks just like if I wanted to create a merkle root. However, we do something more. What is that more? I am going to take the block, split it into chunks, but then code those chunks. That seems simple. Take the block, split it into chunks, and then code those chunks. So you’re adding some parity and extra information to bring the redundancy you require. Now this is not enough. If you just did this, it turns out that you don’t get these optimal results. What you have to do is you have to build a hierarchy of this construction. What is the hierarchy? You take each of these chunks in the lowest layer, take the hash of them, just like you would if you did a merkle tree. You take the hash of each of these, those are the small chunks up there, and you erasure code those hashes. You take hashes from the lowest layer, you code those hashes, now you have another layer and exactly the same thing happens again. You keep doing this until you get to the root, which is of constant size.

You take a block, split it into chunks, create coded chunks, take hashes, create coded hashes, and recurse hierarchically. It’s very similar to the merkle tree if you didn’t do the encoding. The merkle tree is used for fraud proofs and membership. It can be used to give data availability proofs. This is our basic algorithm.

# Merkle inclusion proofs

Let me point out how a node samples. Suppose that I want to sample a given chunk. How do I prove that this is the 16th chunk related to that root? A merkle tree gives a membership inclusion proof. To do that, you need to show all the highlighted elements in the graph in this diagram. If I show you all those tree elements, then I am able to establish the relationship between my chunk and the merkle root. This is how you do merkle inclusion proofs.

When you try to sample a chunk, you’re automatically sampling all the different layers. Just sampling a chunk at the lower layers, implies sampling at the higher layer. If you sample a lower chunk, you’re only sampling the hashes and you’re never sampling the codes of those hashes. However, because of the way we interleave the hashes, what you will see is you’re also touching some of these coded hashes. It offers an extra layer of sampling when you sample a chunk.

# Coded merkle tree advantage

Suppose you are an honest full node. You’re a node in the shard which downloaded the various chunks. Remember, some of these chunks may be unavailable which is why we do the erasure codes. You keep hearing what the other nodes are saying. Is it possible for you to extrapolate the entire tree? What you can do is you can essentially decode layer by layer. You decode the first layer, because that’s an erasure code and you should be able to extrapolate that, and now that you have those commitments you can decode and verify the next layer and do it again on the next layer.

At one layer, maybe you find an inconsistent parity. If this is the case, then you can go and inform the other nodes that this has a parity violation at the last but one layer or whatever. Okay? So why is this interesting? This is interesting because the proof that there is a parity violation can now be constant sized. It’s only a constant number of these chunks.

That’s the main result. To make this coded merkle tree work, we have three main ideas. The first one is to make sure that your fraud proof size is small, there needs to be low-density parity check codes where each of the parity equations each have a constant number of symbols. Second, when you decode a code, you need to be able to infer proofs of membership of these symbols. You need a mechanism by which you can iteratively reconstruct and prove the membership, which the coded merkle tree offers. The hierarchy, finally, provides efficiency.

The coded merkle tree achieves optimal header size, sampling cost, coded-fraud proof size, and decoding complexity. We have an implementation of this in a rust library.

https://github.com/songZLi/coded_merkle_tree

# Closing the loop on sharding

The fact that you use this coded merkle tree library essentially ensures that you only take a logarithmic hit in communication cost imposed on the main chain. The overhead for storage and computation become O(log k). If you use some of the other earlier scheme,s you will not get optimal scaling you will only get sqrt(k) scaling.

# Targeted liveness attack

So we took data availability article, plugged it back into our original scheme, and the claim is that it has solved the sharding problem. The story is a little bit more intricate… I’m not going to talk about those aspects, but you might notice on what needs to be done… Since you’re allowing free shard allocation where each node can decide which shard to belong to in a democratic way, what happens is all the adversaries can congregate into a shard. As I pointed out, this does not give you a safety violation. However, you can have a liveness violation because almost all the blocks in the shard may now be manufactured by adversaries… so we call this a “targeted liveness attack”. What will happen is that the adversary can congregate on a worst-case shard and completely drown your throughput. To design your system to handle the worst case situation, you can only handle a throughput of O(1) and we have a bunch of interesting ideas to basically solve this problem.

# Summary

I’ll go to the main result. After including these ideas, you get a new sharding proposal based on coded merkle tree, and it’s able to handle a fully adaptive adversary and guarantee you that the throughput is scaling almost linearly while imposing very minimal storage and communication overhead. With that, I conclude my talk thank you.

*Sponsorship*: These transcripts are sponsored by Blockchain Commons.

*Disclaimer*: These are unpaid transcriptions, performed in real-time and in-person during the actual source presentation. Due to personal time constraints they are usually not reviewed against the source material once published. Errors are possible. If the original author/speaker or anyone else finds errors of substance, please email me at kanzure@gmail.com for corrections or contribute online via github/git. I sometimes add annotations to the transcription text. These will always be denoted by a standard editor’s note in parenthesis brackets ((like this)), or in a numbered footnote. I welcome feedback and discussion of these as well.

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