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papers/lux-fpc-consensus/sections/06-pseudorandom-function-for-stability.tex
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\section{Pseudorandom Function for Stability}
\label{sec:prf}
FPC uses a cryptographic PRF to ensure deterministic thresholds:
\begin{lstlisting}[language=Go, caption=PRF-based threshold stability]
func deterministicThreshold(round int, seed []byte) float64 {
input := append(seed, uint64ToBytes(round)...)
hash := blake3.Sum256(input)
// Map hash to [0, 1]
val := binary.BigEndian.Uint64(hash[:8])
normalized := float64(val) / float64(^uint64(0))
// Scale to [thetaMin, thetaMax]
return thetaMin + (thetaMax-thetaMin)*normalized
}
\end{lstlisting}
This provides:
\begin{itemize}
\item \textbf{Determinism}: Same threshold for given round across honest nodes
\item \textbf{Testability}: Reproducible simulations
\item \textbf{Security}: Prevents adversarial threshold manipulation
\end{itemize}