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zeekay
abf99d05fc
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.
54 lines
1.4 KiB
TeX
54 lines
1.4 KiB
TeX
\section{Future Enhancements}
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\subsection{Post-Quantum Verkle Trees}
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Research directions for quantum-resistant variants:
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\subsubsection{Lattice-Based Commitments}
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Using Learning With Errors (LWE):
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\begin{equation}
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C = As + e \bmod q
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\end{equation}
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where $A$ is public matrix, $s$ is secret, $e$ is error.
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\subsubsection{Hash-Based Accumulators}
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Merkle trees with stateless hash-based signatures:
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\begin{equation}
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\pi_{SPHINCS} = (auth_{path}, OTS_{signature})
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\end{equation}
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\subsection{Optimized Trusted Setups}
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\subsubsection{Updatable Reference Strings}
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Allow adding new participants post-ceremony:
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\begin{equation}
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\mathsf{SRS}_{new} = \mathsf{Update}(\mathsf{SRS}_{old}, \tau_{new})
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\end{equation}
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\subsubsection{Transparent Setup}
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Using class groups or unknown-order groups:
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\begin{equation}
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g^{2^{2^t}} \bmod N
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\end{equation}
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where factorization of $N$ is unknown.
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\subsection{Adaptive Tree Arity}
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Dynamic width adjustment based on access patterns:
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\begin{equation}
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w_{optimal} = \argmin_{w} \left( d(w) \cdot \log w + \frac{P_{proof}}{w} \right)
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\end{equation}
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For hot paths, increase width to reduce depth.
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\subsection{Cross-Chain Proof Aggregation}
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Aggregate proofs across multiple chains:
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\begin{equation}
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\pi_{aggregate} = \mathsf{Aggregate}(\pi_{P-chain}, \pi_{C-chain}, \pi_{X-chain})
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\end{equation}
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Single proof verifies state across entire Lux network.
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