papers/lux-universal-threshold-signatures/sections/04-multi-chain-adapter-architecture.tex

\section{Multi-Chain Adapter Architecture}


\subsection{Unified Interface}

We define a chain-agnostic interface abstracting signature operations:

\begin{algorithmic}[1]
\State \textbf{function} \textsc{SignerAdapter}()
\State \textbf{Digest}$(tx) \to$ hash: Compute chain-specific message digest
\State \textbf{SignEC}$(hash, share) \to$ partial: Generate partial signature
\State \textbf{AggregateEC}$(partials) \to$ signature: Combine partial signatures
\State \textbf{Encode}$(signature) \to$ bytes: Format for blockchain submission
\State \textbf{FormatPublicKey}$(point) \to$ address: Derive chain address

\end{algorithmic}

\subsection{Chain-Specific Adapters}

\subsubsection{XRPL Adapter}

XRP Ledger requires specific hash prefixes and signature normalization:

\paragraph{Hash Prefixes}
\begin{itemize}
\item \textbf{Single-signing}: STX prefix (0x53545800)
\item \textbf{Multi-signing}: SMT prefix (0x534D5400)
\end{itemize}

\paragraph{Hash Function} SHA-512Half (first 256 bits of SHA-512):
\begin{align*}
\text{digest} = \text{SHA-512Half}(\text{prefix} || \text{tx\_blob})
\end{align*}

\paragraph{Signature Normalization} XRPL requires low-S values:
\begin{algorithmic}[1]
\If{$s > q/2$}
    \State $s \leftarrow q - s$
\EndIf
\end{algorithmic}

\paragraph{Public Key Format}
\begin{itemize}
\item ECDSA: 33-byte compressed (0x02/0x03 prefix)
\item EdDSA: ED prefix (0xED) + 32-byte public key
\end{itemize}

\subsubsection{Ethereum Adapter}

Support for legacy and modern transaction types:

\paragraph{Transaction Types}
\begin{itemize}
\item \textbf{Legacy}: RLP encoding, EIP-155 chain ID in signature
\item \textbf{EIP-1559}: Base fee + priority fee, type 0x02
\item \textbf{EIP-4844}: Blob transactions, type 0x03
\end{itemize}

\paragraph{Signature Encoding}
\begin{align*}
v &= \begin{cases}
27 + \text{recovery\_id} & \text{(pre-EIP-155)} \\
35 + 2 \cdot \text{chainID} + \text{recovery\_id} & \text{(EIP-155)}
\end{cases}
\end{align*}

\paragraph{Contract Wallet Support} EIP-1271 signature verification for smart contract wallets via \texttt{isValidSignature} interface.

\subsubsection{Bitcoin Adapter}

Support for legacy, SegWit, and Taproot:

\paragraph{Signature Hash Types}
\begin{itemize}
\item SIGHASH\_ALL (0x01): Sign all inputs and outputs
\item SIGHASH\_SINGLE (0x03): Sign corresponding output
\item SIGHASH\_ANYONECANPAY (0x80): Sign only one input
\end{itemize}

\paragraph{Taproot (BIP-340)} Schnorr signatures with:
\begin{itemize}
\item x-only public keys (32 bytes, even y)
\item Tagged hashes: $H(\text{tag} || \text{tag} || m)$
\item Signature: $(R_x, s)$ where $R_x$ is x-coordinate
\end{itemize}

\paragraph{PSBT Support} Partially Signed Bitcoin Transactions enable collaborative signing workflow.

\subsubsection{Solana Adapter}

EdDSA signatures with Program Derived Addresses (PDAs):

\paragraph{Message Format}
\begin{algorithmic}[1]
\State Header: numSignatures, numReadonly, numReadonlyUnsigned
\State Account keys: $[\text{pubkey}_1, \ldots, \text{pubkey}_n]$
\State Recent blockhash (32 bytes)
\State Instructions: program ID, accounts, data
\end{algorithmic}

\paragraph{PDA Derivation}
\begin{align*}
\text{PDA} = H(\text{seeds} || \text{program\_id} || \text{``ProgramDerivedAddress''})
\end{align*}
where $H$ outputs a point off the Ed25519 curve.

\paragraph{Versioned Transactions} Support for address lookup tables (v0 transactions).

\subsubsection{TON Adapter}

Bag of Cells (BOC) serialization with EdDSA:

\paragraph{Cell Structure}
\begin{itemize}
\item Hash: SHA-256 of cell representation
\item Depth: Maximum reference depth
\item References: Up to 4 child cells
\item Data: Up to 1023 bits
\end{itemize}

\paragraph{Workchain Support} TON uses multiple workchains (basechain = 0, masterchain = -1).

\subsubsection{Cardano Adapter}

Multi-era support (Byron, Shelley, Allegra, Mary, Alonzo, Babbage):

\paragraph{Signature Schemes}
\begin{itemize}
\item EdDSA: Standard signing
\item ECDSA: secp256k1 for interoperability
\item Schnorr: Taproot-style signatures
\end{itemize}

\paragraph{Plutus Scripts} Smart contracts require witness sets with redeemers and datums.

\paragraph{Multi-Signature} Native multi-sig scripts with AND/OR logic.

\subsection{Performance Comparison}

\begin{table}[h]
\centering
\small
\begin{tabular}{@{}lcccc@{}}
\toprule
\textbf{Chain} & \textbf{Sig Type} & \textbf{Hash} & \textbf{Encode} & \textbf{Total} \\
\midrule
XRPL & ECDSA & 1.2ms & 0.3ms & 1.5ms \\
Ethereum & ECDSA & 0.8ms & 0.4ms & 1.2ms \\
Bitcoin & Schnorr & 0.9ms & 0.2ms & 1.1ms \\
Solana & EdDSA & 1.1ms & 0.5ms & 1.6ms \\
TON & EdDSA & 1.4ms & 0.6ms & 2.0ms \\
Cardano & EdDSA & 1.0ms & 0.4ms & 1.4ms \\
\bottomrule
\end{tabular}

\label{tab:adapter_performance}
\end{table}