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20 lines
1.1 KiB
TeX
20 lines
1.1 KiB
TeX
\section{Validator Set Management}
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\subsection{Stake-Weighted Selection}
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Validators are selected proportionally to their staked $\textsc{Keeper}$ tokens. The probability of validator $v_i$ being included in the active set of size $k$ is:
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\begin{equation}
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P(v_i \in \mathcal{A}) = 1 - \left(1 - \frac{w_i}{W}\right)^k
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\end{equation}
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For validators with significant stake ($w_i / W \geq 1/k$), inclusion is near-certain.
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\subsection{Epoch Transitions and DKG}
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Validator sets rotate every epoch ($E = 1000$ blocks). At epoch boundary $h_e$: (1)~compute $\mathcal{V}_{e+1}$ from staking state at $h_e - 100$; (2)~execute \Corona{} distributed key generation for the new set; (3)~BLS keys persist (no DKG needed); (4)~transition at $h_e + 1$ with 10-block overlap.
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The \Corona{} DKG has each validator $v_i$ sample polynomial $f_i(x) = \sum_{j=0}^{t-1} a_{i,j} x^j$ over $R_q$, broadcast commitments, and send encrypted shares to peers. The collective public key is $PK = \sum_{i=1}^{n} C_{i,0}$. The protocol completes in 3 rounds with $O(n^2)$ messages ($\sim$7.6\,GB for $n = 1000$).
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