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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.
73 lines
2.1 KiB
TeX
73 lines
2.1 KiB
TeX
\section{Lux Implementation}
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\subsection{Integration Architecture}
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Lux's multi-chain architecture requires Verkle tree integration at three levels:
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\begin{enumerate}
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\item \textbf{P-Chain}: Platform chain managing validators and appchains
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\item \textbf{C-Chain}: EVM-compatible contract chain
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\item \textbf{X-Chain}: UTXO-based exchange chain
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\end{enumerate}
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\subsection{P-Chain State Model}
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The P-Chain maintains:
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\begin{itemize}
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\item Validator sets: $\mathcal{V} = \{(pk_i, stake_i, end_i)\}$
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\item Delegations: $\mathcal{D} = \{(del_i, val_i, amount_i)\}$
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\item Appchain configurations: $\mathcal{S} = \{(id_i, params_i)\}$
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\end{itemize}
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Verkle commitment:
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\begin{equation}
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C_{P} = \mathsf{Commit}(\mathcal{V} || \mathcal{D} || \mathcal{S})
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\end{equation}
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\subsection{C-Chain EVM Integration}
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EVM state comprises:
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\begin{itemize}
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\item Account states: nonce, balance, storageRoot, codeHash
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\item Contract storage: key-value mappings
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\item Contract code: bytecode blobs
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\end{itemize}
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Account encoding in Verkle tree:
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\begin{equation}
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\mathsf{Account}(addr) = \{nonce || balance || code_{hash} || storage_{root}\}
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\end{equation}
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Storage slot mapping:
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\begin{equation}
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\mathsf{StorageKey}(addr, slot) = \mathsf{Hash}(addr || slot)
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\end{equation}
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\subsection{State Transition Proofs}
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For transaction $tx$ modifying state from $S$ to $S'$:
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\begin{equation}
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\pi_{transition} = (\pi_{pre}, \pi_{post}, \pi_{witnesses})
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\end{equation}
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where:
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\begin{itemize}
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\item $\pi_{pre}$: Proofs for pre-state values
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\item $\pi_{post}$: Proofs for post-state values
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\item $\pi_{witnesses}$: Auxiliary data (e.g., code proofs)
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\end{itemize}
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\subsection{Cross-Chain Verification}
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Appchain validators verify cross-chain transfers using Verkle proofs:
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\begin{algorithmic}[1]
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\STATE \textbf{function} $\mathsf{VerifyCrossChain}(proof, sourceRoot, targetRoot)$
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\STATE $valid_{source} \gets \mathsf{VerifyProof}(proof.source, sourceRoot)$
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\STATE $valid_{target} \gets \mathsf{VerifyProof}(proof.target, targetRoot)$
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\STATE \textbf{return} $valid_{source} \land valid_{target}$
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\end{algorithmic}
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