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An essential primitive in distributed systems is broadcast, or the ability to send a group of participants the same message. In the honest case, this problem is straightforward; send everyone the message and acknowledge its receipt. However, this problem becomes complicated under the assumption of byzantine faults. If we apply the honest protocol to the byzantine environment, we may have different peers accept different values! In this article, I give a summary and implementation of an algorithm for overcoming the problem.

## The Problem

The problem we are trying to solve is that of reliable broadcast. Specifically, we want a broadcast protocol that guarantees all processes accept the same value (or none) as the result of a broadcast within a closed group.

In this instance we consider the byzantine fault model. That is, in a system of $n$ processes, $n \geq 3f+1$, where $f$ faulty processes can behave arbitrarilty. Our only assumption is that honest peers obey the protocol.

The other type of failure model usually considered is that of the network. That is out of scope for this article. We will simply assume here that messages from honest peers are delivered eventually. Later, I will show how the implementation copes with messages from dishonest (byzantine) peers. Then we will see that exactly-once delivery of messages from honest peers is nice, but not required.

## The Code

If you would like to follow along during this post, the code can be found at https://github.com/cnnrznn/clj-net.git. The code for this post is located in the src/clj_net/broadcast.clj file. The project is written in Clojure which is a beautiful functional language that is also practical as it runs on the JVM and has access to the Java ecosystem. If you wish to run the code, you’ll need Leiningen.

For testing, I have a Dockerfiles located in test/docker. First, build the image from context-base as base, then build the image from context as bb (or edit run-container.sh). Finally, you need to create a custom network so the run-container.sh script can assign static IP’s.

Throughout the code you will see a number of functions with the suffix -func. This is my naming convention for functions that return functions. Specifically, for this protocol I wanted to parameterize certain functions by the current initiator and round. This way, I don’t have to pass them as parameters every time. For example, by calling (validate-func initiator round) I create a validate function that only accepts messages tagged with that initiator and round. Neat!

## The Solution

The solution to the broadcast problem is to insert another layer in the stack: a reliable broadcast primitive. The goal of the primitive is to reduce the power of byzantine processes to that of fail-stop processes. Two properties must hold for a process $p$ broadcasting message $v$:

1. Validity If $p$ is correct, all correct processes accept $v$
2. Agreement If $p$ is faulty, then either all correct processes accept the same value, or no value is accepted from $p$

This protocol comes from an old paper by Gabriel Bracha Asynchronous Byzantine Agreement Protocols. After establishing this primitive, Bracha uses it to achieve a randomized consensus algorithm resilient to $n \geq 3f+1$ faults!

The protocol has 3 phases:

1. The initiator broadcasts its message to all peers
2. The peers echo this message to indicate what they think the value is
3. The peers send ready messages to indicate a commit

## Phases

### Initial

The sender simply broadcasts its message to the peers.

If you are following along in the code See the function broadcast-func.

### Echo

All peers wait for either

1. $1$ initial message
2. $2f+1$ echo messages
3. $f+1$ ready messages

When any of these occur, the process broadcasts an echo messages to all peers.

For the peer, a single initial message is sufficient to echo the value. However, if we want to send an echo based on other echo messages, we need to wait for $2f+1$ echoes. Why? If we have $2f+1$ matching echoes, we know that a minimum of $f+1$ honest peers have also sent an echo for the same value. This means that a majority of honest nodes must have received the same initial message.

Likewise, we can send an echo if we have heard $f+1$ ready messages. Why do we need $2f+1$ echoes but only $f+1$ ready messages? In order to send a ready message, a correct process must have received $2f+1$ echo messages. So, we can use the fact that at least one correct process has received enough echoes in order to send our own.

All processes wait for

1. $2f+1$ echo messages
2. $f+1$ ready messages

As above, these qualities indicate that a majority of honest nodes have received the same initial message, and therefore the same value. Once either of these are fulfilled, the process broadcasts a ready message.

### Accept

Finally, the process waits for $2f+1$ ready messages. Once it has them, it knows a majority of hones nodes are also planning to accept the value.

## Implementation Details

### Message Format

The messages in the system have four components

• initiator- PID of the protocol initiator
• sender - PID of the sender of this message
• round - round identifier
• value - payload
• type - initial, echo, ready

The sender indicates the initiator of the broadcast protocol. The round is a number used to totally order broadcasts from a single process. The value is the proposed result of the broadcast. The type of the message indicates in what phase of the protocol the message was sent.

It should be noted that in a production environment, messages should be authenticated with cryptographic signatures. For this implementation, it is sufficient for demonstration and testing to assign messages the sender field as an integer.

## Future Work

At the time of writing there are a number of limitations that the code has which I’m not sure if I will have time to address.

1. No retransmission (core.clj)
2. Messages for different (initiator, round) pairs are simply forgotten
3. No proper authentication

## Conclusion

In this post, I summarize and present the implementation for a byzantine resilient broadcast protocol. The protocol consists of three phases which guarantee that all correct (honest) nodes either receive the same value or no value at all. It also guarantees that if the broadcasting process is correct, the value is guaranteed to be received and accepted by all other correct processes (under our system assumptions). This reliable broadcast primitive can be used to implement other distributed protocols, such as atomic broadcast.

Implementing this protocol was helpful towards realizing what details are left out by the paper, and what other assumptions cannot remain simply that. For example, papers can claim “messages get delivered eventually” which is helpful to precisely $0$ implementations. Now you’re saying to yourself, “Wait a second, you said this was for future work?” Precisely. My implementation will probably break under the slightest perturbation.

Enjoy. Maybe some day I’ll get around to making this robust ;)

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