# Weak Causal Probabilistic Reliable Broadcast

The main responsibility of the TCE network is to execute a broadcast primitive named the Weak Causal Probabilistic Reliable Broadcast (WCPRB) that propagates and securely delivers certificates across the Topos ecosystem to prevent conflicting certificates.

By its consensusless nature, the WCPRB is a simpler, more efficient and more robust implementation than consensus-based solution, which is important from a security perspective. The protocol is permissionless and allows for dynamic reconfiguration.

The WCPRB exposes the following interface:

• broadcast(m): used by a process inside the system to broadcast a message m.
• deliver(p,m): used by a process inside the system to handle the delivery of a message m from sender p.

And satisfies the following key properties:

Integrity: For all processes p and message m, an honest process executes deliver(p, m) at most once and, if p is honest, only if p executed broadcast(m).

Validity: If p and q are honest and p executes broadcast(m), then q executes deliver(p,m).

Agreement: If p and q are honest processes and p execute deliver(r,m), then q executes deliver(r,m).

Source ordering: If p and q are honest processes and both execute deliver(r,m) and deliver(r,m'), then they do so in the same relative order.

## Setup​

To correctly execute the WCPRB protocol, TCE nodes locally hold the following variables:

history(S_j): The local set of accepted incoming and outgoing certificates involving subnet S_j.

digest(S_i): The local set of incoming certificates involving subnet S_i since its last outgoing certificate.

mempool: The local set of certificates pending for acceptation (not yet accepted nor included).

##### tip

A certificate is incoming if it contains a cross-subnet transaction addressed to the corresponding subnet, and outgoing if produced by the corresponding subnet.

## Sampling​

A new TCE node, once it has joined the TCE network, has successfully built three samples of peers:

• An Echo sample $\mathcal{E}$ and its associated threshold $E < \vert \mathcal{E} \vert$
• A Ready sample $\mathcal{R}$ and its associated threshold $R < \vert \mathcal{R} \vert$
• A Delivery sample $\mathcal{D}$ and its associated threshold $D < \vert \mathcal{D} \vert$

Starting from this basis, a TCE node starts exchanging sample-specific subcription messages with its Echo and Ready peers.

Upon receiving sample-specific subscription messages from other nodes, a TCE node adds the corresponding message senders in new samples in the following manner:

• Senders of Echo subscription messages are added to a new $\tilde \mathcal{E}$ set;
• Senders of Ready subscription messages are added to a new $\tilde \mathcal{R}$ set.

A TCE node interacts with its samples as follows:

• It only listens for messages coming from peers in samples $\mathcal{E}$, $\mathcal{R}$, and $\mathcal{D}$;
• It only sends messages to peers in sets $\tilde \mathcal{E}$ and $\tilde \mathcal{R}$.
##### tip

In the TCE, the per-node communication is logarithmic in the size of the system and the overall communication complexity of the system is quasilinear, which allows the TCE to seamlessly scale to billions of processes.

## Protocol overview​

To submit a certificate Cert, the subnet broadcasts a message m = (Cert, digest(S_j)) to the TCE nodes it is connected to. Upon receiving this message, the TCE nodes propagate it to the rest of the TCE network via gossip.

##### Reminder

digest(S_j) contains incoming (from the point of view of subnet S_j) certificates sent by other subnets since S_j's last certificate.

The ICE-FROST signed message m eventually reaches all the TCE nodes. After a correct node receives m, it verifies the message signature and if correct, it sends an Echo message to all nodes in its $\tilde \mathcal{E}$ set.

Each correct node issues a Ready message to all the nodes in $\tilde \mathcal{R}$​ if it has received more than $E$ Echo (resp. $R$ Ready) messages from $\mathcal{E}$ (resp. $\mathcal{R}$).

At this point, the message containing the certificate is yet to be delivered. In order for a correct node to deliver the message, it needs to have received more than $D$ Ready messages from its delivery sample $\mathcal{D}$.

Upon delivery, a correct node checks if m is well-formed, and then adds it to the pool of messages pending validation mempool.

Before applying the certificate from subnet S_j​ to its state, a correct TCE node validates the certificate via the certificate validation function.

Once a certificate passes validation, the TCE node applies the certificate to its local state. Applying a certificate means that the TCE node adds the certificate Cert and its digest digest(S_j) to the history of subnet S_j​.

##### Amplification step

Having the ready sample $\mathcal{E}$ is paramount for the totality property of the WCPRB, as it creates a feedback loop. Consequently, either all correct processes will eventually deliver m, or none of them will.