Bitcoin : Distributed consensus

In a generic manner, centralization and decentralization. Let’s now examine decentralization in Bitcoin at a more technical level. A key term that will come up throughout this discussion is consensus, and specifically, distributed consensus. The key technical problem to solve in building a distributed e‐cash system is achieving distributed consensus. Intuitively, you can think of our goal as decentralizing ScroogeCoin, the hypothetical currency.

Distributed consensus has various applications, and it has been studied for decades in computer science. The traditional motivating application is reliability in distributed systems. Imagine you’re in charge of the backend for a large social networking company like Facebook. Systems of this sort typically have thousands or even millions of servers, which together form a massive distributed database that records all of the actions that happen in the system. Each piece of information must be recorded on several different nodes in this backend, and the nodes must be in sync about the overall state of the system.

The implications of having a distributed consensus protocol reach far beyond this traditional application. If we had such a protocol, we could use it to build a massive, distributed key‐value store, that maps arbitrary keys, or names, to arbitrary values. A distributed key‐value store, in turn, would enable many applications. For example, we could use it to build a distributive domain name system, which is simply a mapping between human understandable domain names to IP addresses. We could build a public key directory, which is a mapping between email addresses (or some other form of real‐world identity) to public keys.

That’s the intuition of what distributed consensus is, but it is useful to provide a technical definition as this will help us determine whether or not a given protocol meets the requirements.

Distributed consensus protocol. There are n nodes that each have an input value. Some of these nodes are faulty or malicious. A distributed consensus protocol has the following two properties:

  • It must terminate with all honest nodes in agreement on the value
  • The value must have been generated by an honest node

What does this mean in the context of Bitcoin? To understand how distributed consensus could work in Bitcoin, remember that Bitcoin is a peer‐to‐peer system. When Alice wants to pay Bob, what she actually does is broadcast a transaction to all of the Bitcoin nodes that comprise the peer‐to‐peer network. See Figure 2.1.

Incidentally, you may have noticed that Alice broadcasts the transaction to all the Bitcoin peer‐to‐peer nodes, but Bob’s computer is nowhere in this picture. It’s of course possible that Bob is running one of the nodes in the peer‐to‐peer network. In fact, if he wants to be notified that this transaction did in fact happen and that he got paid, running a node might be a good idea. Nevertheless, there is no requirement that Bob be listening on the network; running a node is not necessary for Bob to receive the funds. The bitcoins will be his whether or not he’s operating a node on the network.

What exactly is it that the nodes might want to reach consensus on in the Bitcoin network? Given that a variety of users are broadcasting these transactions to the network, the nodes must agree on

exactly which transactions were broadcast and the order in which these transactions happened. This will result in a single, global ledger for the system. Recall that in ScroogeCoin, for optimization, we put transactions into blocks. Similarly, in Bitcoin, we do consensus on a block‐by‐block basis.

So at any given point, all the nodes in the peer‐to‐peer network have a ledger consisting of a sequence of blocks, each containing a list of transactions, that they’ve reached consensus on.             Additionally, each node has a pool of outstanding transactions that it has heard about but have not yet been included on the block chain. For these transactions, consensus has not yet happened, and so by definition, each node might have a slightly different version of the outstanding transaction pool. In practice, this occurs because the peer‐to‐peer network is not perfect, so some nodes may have heard about a transaction that other nodes have not heard about.

How exactly do nodes come to consensus on a block? One way to do this: at regular intervals, say every 10 minutes, every node in the system proposes its own outstanding transaction pool to be the next block. Then the nodes execute some consensus protocol, where each node’s input is its own proposed block. Now, some nodes may be malicious and put invalid transactions into their blocks, but we might assume that other nodes will be honest. If the consensus protocol succeeds, a valid block  will be selected as the output. Even if the selected block was proposed by only one node, it’s a valid output as long as the block is valid. Now there may be some valid outstanding transaction that did not get included in the block, but this is not a problem. If some transaction somehow didn’t make it into this particular block, it could just wait and get into the next block.

The approach in the previous paragraph has some similarities to how Bitcoin works, but it’s not quite how it works. There are a number of technical problems with this approach. Firstly, consensus in general is a hard problem since nodes might crash or be outright malicious. Secondly, and specifically in the Bitcoin context, the network is highly imperfect. It’s a peer‐to‐peer system, and not all pairs of nodes are connected to each other. There could be faults in the network because of poor Internet connectivity for example, and thus running a consensus protocol in which all nodes must participate is not really possible. Finally, there’s a lot of latency in the system because it’s distributed all over the Internet.

Sidebar: The Bitcoin protocol must reach consensus in the face of two types of obstacles: imperfections in the network, such as latency and nodes crashing, as well as deliberate attempts by some nodes to subvert the process.

One particular consequence of this high latency is that there is no notion of global time. What this means is that not all nodes can agree to a common ordering of events simply based on observing timestamps. So the consensus protocol cannot contain instructions of the form, “The node that sent the first message in step 1 must do X in step 2.” This simply will not work because not all nodes will agree on which message was sent first in the step 1 of the protocol.

Impossibility results. The lack of global time heavily constrains the set of algorithms that can be used in the consensus protocols. In fact, because of these constraints, much of the literature on distributed

consensus is somewhat pessimistic, and many impossibility results have been proven. One very well known impossibility result concerns the Byzantine Generals Problem. In this classic problem, the Byzantine army is separated into divisions, each commanded by a general. The generals communicate by messenger in order to devise a joint plan of action. Some generals may be traitors and may intentionally try to subvert the process so that the loyal generals cannot arrive at a unified plan. The goal of this problem is for all of the loyal generals to arrive at the same plan without the traitorous generals being able to cause them to adopt a bad plan. It has been proven that this is impossible to achieve if one‐third or more of the generals are traitors.

A much more subtle impossibility result, known for the names of the authors who first proved it, is called the Fischer‐Lynch‐Paterson impossibility result. Under some conditions, which include the nodes acting in a deterministic manner, they proved that consensus is impossible with even a single faulty process.

Despite these impossibility results, there are some consensus protocols in the literature. One of the better known among these protocols is Paxos. Paxos makes certain compromises. On the one hand, it never produces an inconsistent result. On the other hand, it accepts the trade‐off that under certain conditions, albeit rare ones, the protocol can get stuck and fail to make any progress.

Breaking traditional assumptions. But there’s good news: these impossibility results were proven in a very specific model. They were intended to study distributed databases, and this model doesn’t carry over very well to the Bitcoin setting because Bitcoin violates many of the assumptions built into the models. In a way, the results tell us more about the model than they do about the problem of distributed consensus.

Ironically, with the current state of research, consensus in Bitcoin works better in practice than in theory. That is, we observe consensus working, but have not developed the theory to fully explain why it works. But developing such a theory is important as it can help us predict unforeseen attacks and problems, and only when we have a strong theoretical understanding of how Bitcoin consensus works will we have strong guarantees Bitcoin’s security and stability.

What are the assumptions in traditional models for consensus that Bitcoin violates? First, it introduces the idea of incentives, which is novel for a distributed consensus protocol. This is only possible in Bitcoin because it is a currency and therefore has a natural mechanism to incentivize participants to act honestly. So Bitcoin doesn’t quite solve the distributed consensus problem in a general sense, but it solves it in the specific context of a currency system.

Second, Bitcoin embraces the notion of randomness. As we will see in the next two sections, Bitcoin’s consensus algorithm relies heavily on randomization. Also, it does away with the notion of a specific starting point and ending point for consensus. Instead, consensus happens over a long period of time, about an hour in the practical system. But even at the end of that time, nodes can’t be certain that any particular transaction or a block has made it into the ledger. Instead, as time goes on, the probability that your view of any block will match the eventual consensus view increases, and the probability that the views will diverge goes down exponentially. These differences in the model are key to how Bitcoin gets around the traditional impossibility results for distributed consensus protocols.

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