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zeekay
9504b4c3ef
Sweep across the non-Tier-1 paper catalogue (Tier-1 owned by parallel
agent and excluded). All 113 processed papers already had luxcover
wired up; this commit fixes 14 build breakers and produces fresh
PDFs across the catalogue.
Fixes:
- lux-blockchain-scaling-laws: em-dash inside lstlisting -> --
- lux-corona-pq: stale \input pointing at 03-the-corona-scheme renamed
to 03-the-corona-scheme (file already renamed on disk)
- lux-lattice-cryptography-primer: same Corona->Corona rename
- lux-formal-verification-lean4: Lean source uses unicode (×, ∀, ∃, ∈,
∧, ∨, ∩, ≠, ⟨, ⟩, ·, ¬) inside lstlistings. Added a literate map
so listings render the math glyphs without UTF-8 fault.
- lux-id-did-specification: ✓/✗ in tabular replaced with \ding{51}
/ \ding{55} (pifont). Added pifont package.
- lux-ntt-simd-implementation: middle-dot in Go assembly listings;
added literate {·}{\textperiodcentered}.
- lux-ntt-transform: μ, ×, –, — in regular text (no T1 fontenc).
Replaced with $\mu$/$\times$/--/--- via unicode->latex sweep.
- lux-perpetuals-derivatives, lux-quantum-consensus,
lux-quasar-consensus, lux-tee-computing-mesh: same unicode->latex
sweep across body text. Also fixed broken math segment
`$L_{avg} = 10$\times$$` -> `$L_{avg} = 10\times$`.
- lux-zchain: emoji glyphs in roadmap table replaced with
parenthetical text.
- lux-triple-proof-consensus: dropped duplicate \usepackage{geometry}
that clashed with luxcover (geometry option clash).
- pq: defined missing \Rq macro.
PDFs rebuilt for the full Tier-2/3 set.
Excluded (Tier-1, parallel agent): lp-073-pulsar, lp-stricte2epq,
dag-evm-formal, lp-010-quasar-stm-{3,4}, lp-020-quasar-consensus,
lux-institutional-custody, lux-nist-mptc-submission, pqsafe-il5,
pq-rns, plus shared/ and lps/.
66 lines
2.8 KiB
TeX
66 lines
2.8 KiB
TeX
\section{TFHE Bridge Privacy}
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\label{sec:tfhe}
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%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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Lux Bridge integrates threshold fully homomorphic encryption (TFHE) for confidential cross-chain operations, enabling private bridge transfers where amounts and recipients are encrypted.
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\subsection{Confidential Transfer Protocol}
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In a confidential bridge transfer, the following values are encrypted under TFHE before being submitted on-chain:
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\begin{itemize}[leftmargin=1.1em]
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\item \textbf{Amount}: $\hat{a} = \textsc{Enc}(a)$ where $a$ is the transfer amount
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\item \textbf{Recipient}: $\hat{r} = \textsc{Enc}(r)$ where $r$ is the destination address
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\item \textbf{Token type}: Optionally encrypted for multi-asset bridges
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\end{itemize}
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The bridge contract performs \emph{homomorphic balance checks} without decryption:
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\begin{algorithm}[H]
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\caption{Confidential Bridge Lock}
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\begin{algorithmic}[1]
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\Function{ConfidentialLock}{$\hat{a}, \hat{r}, \text{proof}$}
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\State \textbf{require} $\text{FHE.verify}(\hat{a}, \text{proof})$ \Comment{Valid encryption}
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\State $\hat{b} \gets \text{balances}[\text{sender}]$ \Comment{Encrypted balance}
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\State $\hat{c} \gets \text{FHE.gte}(\hat{b}, \hat{a})$ \Comment{Homomorphic comparison}
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\State \textbf{require} gateway.decrypt($\hat{c}$) $= \texttt{true}$ \Comment{Threshold decryption of boolean}
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\State $\text{balances}[\text{sender}] \gets \text{FHE.sub}(\hat{b}, \hat{a})$
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\State Emit encrypted lock event $(\hat{a}, \hat{r}, \text{destChainId})$
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\subsection{Threshold Decryption for Settlement}
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The destination chain MPC committee performs threshold decryption to settle the transfer:
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\begin{enumerate}
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\item Each MPC node $i$ computes a decryption share $d_i = \textsc{PartialDec}(sk_i, \hat{a})$
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\item When $t$ shares are collected: $a = \textsc{Combine}(\{d_i\}_{|S| \geq t})$
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\item Plaintext amount $a$ is minted on the destination chain
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\end{enumerate}
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\textbf{Privacy guarantee}: No individual node (nor any coalition of $< t$ nodes) learns the transfer amount. Only the threshold committee collectively can decrypt, and only at settlement time.
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\subsection{TFHE Parameters}
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\begin{table}[h]
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\centering
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\begin{tabular}{lr}
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\toprule
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\textbf{Parameter} & \textbf{Value} \\
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\midrule
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FHE scheme & TFHE (TaskManager precompile) \\
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Precompile address & \texttt{0xeA30c4B8...D9} \\
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Security level & 128-bit (LWE) \\
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Encrypted types & \texttt{euint64}, \texttt{eaddress}, \texttt{ebool} \\
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Comparison gas & $\sim$200,000 \\
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Threshold decryption & $t$-of-$n$ via Gateway \\
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EVM version required & Cancun (transient storage) \\
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\bottomrule
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\end{tabular}
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\caption{TFHE bridge privacy parameters}
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\end{table}
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%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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