mirror of
https://github.com/lux-apps/papers.git
synced 2026-10-30 18:15:21 +00:00
zeekayandHanzo Dev
178febad68
Every rendered "T-Chain" / "ThresholdVM" / "teleportvm" reference across the paper corpus is rewritten to the correct canonical chain by concern: threshold signing / MPC / bridge custody / key recovery -> M-Chain (MVM); FHE / encrypted compute / threshold decryption -> F-Chain (FVM); teleport / cross-chain messaging -> B-Chain (bridgevm); consensus Pulsar stays Q-Chain. Section lux-trust-kernel/03-t-chain-threshold-governance.tex renamed -> 03-f-chain-encrypted-policy.tex (with \input + xref fixes). Braided "T-Chain" sections split by concern (M vs F). Only lp-020's chain-separation rationale and the shared lux/chains/thresholdvm library path retain the name, to record the removal. All changed papers rebuilt (pdflatex, rc=0, no undefined refs). ยง09 of lux-dao-governance-framework reframed: fabricated "production deployment" metrics ($50M/$240k/$12M, survey %s, "as of Oct 2024") relabeled as illustrative design configurations with no invented replacements; reality noted (DAO treasury is a 1/1 Safe); conclusion echo + one "first production" overclaim softened. This commit also captures concurrent corpus workstreams on the same tree. Co-authored-by: Hanzo Dev <[email protected]>
73 lines
2.5 KiB
TeX
73 lines
2.5 KiB
TeX
\section{Post-Quantum Security}
|
|
|
|
|
|
\subsection{Pulsar Lattice-Based Signatures}
|
|
|
|
Pulsar provides quantum-resistant threshold signatures using Module-LWE hardness assumptions.
|
|
|
|
\paragraph{Security Levels}
|
|
\begin{itemize}
|
|
\item \textbf{Level 1}: 128-bit quantum security (NIST Category 1)
|
|
\item \textbf{Level 3}: 192-bit quantum security (NIST Category 3)
|
|
\item \textbf{Level 5}: 256-bit quantum security (NIST Category 5)
|
|
\end{itemize}
|
|
|
|
\paragraph{Key Generation} Distributed sampling of lattice shares:
|
|
\begin{algorithmic}[1]
|
|
\State Sample $\mathbf{A} \xleftarrow{R} R_q^{k \times l}$ (public randomness)
|
|
\State Each party $i$ samples $\mathbf{s}_i \leftarrow \chi_\eta$ (secret share)
|
|
\State Compute $\mathbf{t}_i = \mathbf{A} \mathbf{s}_i + \mathbf{e}_i$ where $\mathbf{e}_i \leftarrow \chi_\eta$
|
|
\State Public key: $\mathbf{t} = \sum_i \mathbf{t}_i$
|
|
\end{algorithmic}
|
|
|
|
\paragraph{Signing} Fiat-Shamir with aborts:
|
|
\begin{algorithmic}[1]
|
|
\State Each party samples $\mathbf{y}_i \leftarrow \chi_\gamma$
|
|
\State Compute commitment $\mathbf{w}_i = \mathbf{A} \mathbf{y}_i$
|
|
\State Aggregate: $\mathbf{w} = \sum_i \mathbf{w}_i$
|
|
\State Challenge: $c = H(\mathbf{w}, m) \in \mathcal{C}$
|
|
\State Response: $\mathbf{z}_i = \mathbf{y}_i + c \mathbf{s}_i$
|
|
\If{$||\mathbf{z}_i|| > B$} \textbf{abort} and restart
|
|
\EndIf
|
|
\State Aggregate: $\mathbf{z} = \sum_i \mathbf{z}_i$
|
|
\State Signature: $(\mathbf{w}, \mathbf{z})$
|
|
\end{algorithmic}
|
|
|
|
\paragraph{Share Refresh} Proactive security via share randomization:
|
|
\begin{algorithmic}[1]
|
|
\State Each party samples $\Delta \mathbf{s}_i \leftarrow \chi_\eta$
|
|
\State Update share: $\mathbf{s}_i' = \mathbf{s}_i + \Delta \mathbf{s}_i$
|
|
\State Broadcast $\Delta \mathbf{t}_i = \mathbf{A} \Delta \mathbf{s}_i + \mathbf{e}_i$
|
|
\State Verify $\sum_i \Delta \mathbf{t}_i = \mathbf{0}$ (public key unchanged)
|
|
|
|
\end{algorithmic}
|
|
|
|
\paragraph{Chain Integration} Pulsar signatures can be verified on-chain via:
|
|
\begin{itemize}
|
|
\item Smart contract verification (Ethereum, Cardano)
|
|
\item Native verification opcodes (future Bitcoin soft fork)
|
|
\item Off-chain verification with on-chain anchoring
|
|
\end{itemize}
|
|
|
|
\subsection{Performance Comparison}
|
|
|
|
\begin{table}[h]
|
|
\centering
|
|
\small
|
|
\begin{tabular}{@{}lccc@{}}
|
|
\toprule
|
|
\textbf{Scheme} & \textbf{Keygen} & \textbf{Sign} & \textbf{Verify} \\
|
|
\midrule
|
|
ECDSA (CMP) & 12ms & 15ms & 2ms \\
|
|
EdDSA (FROST) & 10ms & 8ms & 2ms \\
|
|
Schnorr (FROST) & 10ms & 8ms & 2ms \\
|
|
Pulsar-128 & 45ms & 120ms & 35ms \\
|
|
Pulsar-192 & 68ms & 180ms & 52ms \\
|
|
Pulsar-256 & 95ms & 240ms & 70ms \\
|
|
\bottomrule
|
|
\end{tabular}
|
|
|
|
\label{tab:pq_performance}
|
|
\end{table}
|
|
|