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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.
61 lines
3.7 KiB
TeX
61 lines
3.7 KiB
TeX
\section{Gas Cost Analysis}
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\label{sec:gas}
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% ============================================================
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A critical advantage of threshold signatures over multisig is constant on-chain
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verification cost. Table~\ref{tab:gas} compares verification costs.
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\begin{table*}[t]
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\centering
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\small
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\begin{tabular}{@{}lrrrll@{}}
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\toprule
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\textbf{Chain Family} & \textbf{TSS Verify} & \textbf{$k$-of-$n$ Multisig} & \textbf{Savings} & \textbf{Verify Method} & \textbf{Protocol} \\
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\midrule
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Ethereum / EVM & 21,000 + 3,000 & 21,000 + $3{,}000k$ & $(k{-}1) \times 3{,}000$ & \texttt{ecrecover} precompile & CGGMP21 \\
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Bitcoin Taproot & 1 vByte witness & $k \times 64$ vB witness & $(k{-}1) \times 64$ vB & OP\_CHECKSIG (Schnorr) & FROST \\
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Bitcoin Legacy & 1 DER sig & $k$ DER sigs & $(k{-}1)$ sigs & OP\_CHECKMULTISIG & CGGMP21 \\
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Solana & 1 Ed25519 verify & $k$ Ed25519 verifies & $(k{-}1)$ verifies & Ed25519 program & FROST \\
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TON & $\sim$0.005 TON & $\sim$0.005$k$ TON & $(k{-}1) \times 0.005$ & Ed25519 TVM opcode & FROST \\
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Cosmos / IBC & 1 sig verify & $k$ sig verifies & $(k{-}1)$ verifies & \texttt{ed25519\_verify} & FROST \\
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XRPL & 1 ECDSA sig & $k$ signer entries & $(k{-}1)$ entries & Native ECDSA & CGGMP21 \\
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Cardano & 1 Ed25519 verify & $k$ verifies & $(k{-}1)$ verifies & Plutus native & FROST \\
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Polkadot & 1 Sr25519 verify & $k$ verifies & $(k{-}1)$ verifies & Runtime verify & FROST \\
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Sui & 1 Ed25519 verify & $k$ verifies & $(k{-}1)$ verifies & Move native & FROST \\
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Aptos & 1 Ed25519 verify & $k$ verifies & $(k{-}1)$ verifies & Move native & FROST \\
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NEAR & 1 Ed25519 verify & $k$ verifies & $(k{-}1)$ verifies & Runtime verify & FROST \\
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Stellar & 1 Ed25519 verify & $k$ signer weights & $(k{-}1)$ weights & Core verify & FROST \\
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Algorand & 1 Ed25519 verify & $k$ verifies & $(k{-}1)$ verifies & AVM opcode & FROST \\
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Tezos & 1 Ed25519 verify & $k$ verifies & $(k{-}1)$ verifies & Michelson & FROST \\
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TRON & 21,000 + 3,000 & 21,000 + $3{,}000k$ & $(k{-}1) \times 3{,}000$ & TVM ecrecover & CGGMP21 \\
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StarkNet & 1 ECDSA verify & $k$ ECDSA verifies & $(k{-}1)$ verifies & Account verifier & CGGMP21 \\
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\bottomrule
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\end{tabular}
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\caption{On-chain signature verification costs: threshold signature (single verify) vs.\ $k$-of-$n$ multisig. Threshold signatures always cost one single-signature verification regardless of $t$ and $n$. Multisig cost scales linearly in $k$.}
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\label{tab:gas}
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\end{table*}
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\paragraph{Ethereum.} On EVM chains, \texttt{ecrecover} costs 3,000 gas. A
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CGGMP21 threshold signature requires exactly one \texttt{ecrecover} call, verifying
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against the MPC group address: $\texttt{ecrecover}(\text{digest}, \sigma) ==
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\texttt{mpcGroupAddress}$. Individual signers are not visible on-chain; only the
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aggregate key matters for verification. A $k$-of-$n$ Gnosis Safe multisig requires
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$k$ \texttt{ecrecover} calls plus contract overhead ($\sim$40,000 gas base). For
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the Teleport production configuration of $t = 67$, $n = 100$: threshold costs
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24,000 gas (base + 1 ecrecover); equivalent multisig costs 241,000 gas (base + 67
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ecrecover). Savings: 90\%.
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\paragraph{Bitcoin Taproot.} A Taproot key-path spend using FROST requires 64 bytes
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of witness data (one Schnorr signature). An equivalent $k$-of-$n$ using
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OP\_CHECKMULTISIGVERIFY requires $k \times 72$ bytes (DER-encoded ECDSA signatures)
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plus the redeem script. For $t = 5$: FROST uses 64 vB; multisig uses 360+ vB.
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Savings: 82\%.
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\paragraph{Solana.} Ed25519 signature verification on Solana costs approximately
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1,400 compute units. A FROST signature requires one verification. A multisig requires
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$k$ verifications plus program logic overhead ($\sim$5,000 CU base). For $t = 5$:
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FROST costs 6,400 CU; multisig costs 12,000 CU. Savings: 47\%.
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% ============================================================
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