11. Consensus

11.1. BABE digest messages

The Runtime is required to provide the BABE authority list and randomness to the host via a consensus message in the header of the first block of each epoch.

The digest published in Epoch ${\mathcal{{{E}}}}_{{n}}$ is enacted in ${\mathcal{{{E}}}}_{{{n}+{1}}}$. The randomness in this digest is computed based on the all the VRF outputs up to including Epoch ${\mathcal{{{E}}}}_{{{n}-{2}}}$ while the authority set is based on all transaction included up to Epoch ${\mathcal{{{E}}}}_{{{n}-{1}}}$.

The computation of the randomeness seed is described in Epoch-Randomness which uses the concept of epoch subchain as described in host specification and the value ${d}_{{B}}$, which is the VRF output computed for slot ${s}_{{B}}$.

Algorithm 31. Epoch Randomness

\begin{algorithm}
\caption{Epoch-Randomness}
\begin{algorithmic}
    \Require $n > 2$
    \State \textbf{init} $\rho \leftarrow \phi$
    \For{$B$ in \call{SubChain}{$\mathcal{E}_{n-2}$}}
        \State $\rho \leftarrow \rho || d_B$
    \EndFor
    \Return \call{Blake2b}{\call{Epoch-Randomness}{$n-1$}$||n||\rho$}
\end{algorithmic}
\end{algorithm}

where ${n}$ is the epoch index.