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Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
89 lines
2.0 KiB
TeX
89 lines
2.0 KiB
TeX
\section{Data Availability Solutions}
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Data availability is crucial for fraud proof security, with various approaches offering different trade-offs.
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\subsection{Full On-chain Data}
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Posting all data on-chain provides maximum security:
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\begin{equation}
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\text{Security}_{\text{on-chain}} = \text{Security}_{\text{L1}}
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\end{equation}
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However, costs scale linearly with data size:
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\begin{equation}
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\text{Cost}_{\text{on-chain}} = \text{DataSize} \times \text{GasPrice}
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\end{equation}
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\subsection{Data Availability Committees}
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DACs reduce costs through trusted committees:
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\begin{definition}[DAC Security]
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A DAC with $n$ members and threshold $t$ provides security:
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\begin{equation}
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P(\text{data available}) = \sum_{k=t}^{n} \binom{n}{k} p^k (1-p)^{n-k}
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\end{equation}
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where $p$ is the probability each member is honest.
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\end{definition}
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\subsection{Lux Appchains as DA Layer}
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Lux appchains can serve as specialized DA layers:
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\begin{enumerate}
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\item \textbf{Dedicated Storage}: Appchain validators store rollup data
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\item \textbf{Sampling Verification}: Light clients sample availability
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\item \textbf{Economic Security}: Validators stake LUX tokens
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\item \textbf{Cross-appchain Verification}: Multiple appchains for redundancy
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\end{enumerate}
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\subsection{Cost-Security Trade-offs}
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Different DA solutions offer varying trade-offs:
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\begin{figure}[h]
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\centering
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\begin{tikzpicture}
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\begin{axis}[
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xlabel={Security Level},
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ylabel={Cost per MB},
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xmin=0, xmax=100,
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ymin=0, ymax=1000,
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legend pos=north west,
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grid=major
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]
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\addplot[color=blue, mark=*] coordinates {
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(100, 1000)
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(95, 500)
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(90, 250)
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(80, 100)
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(70, 50)
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};
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\addlegendentry{On-chain}
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\addplot[color=red, mark=square*] coordinates {
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(90, 100)
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(85, 80)
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(80, 60)
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(70, 40)
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(60, 20)
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};
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\addlegendentry{DAC}
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\addplot[color=green, mark=triangle*] coordinates {
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(95, 200)
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(90, 150)
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(85, 100)
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(75, 70)
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(65, 40)
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};
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\addlegendentry{Lux Appchain}
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\end{axis}
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\end{tikzpicture}
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\caption{Cost vs Security for different DA solutions}
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\end{figure}
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