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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.
74 lines
3.2 KiB
TeX
74 lines
3.2 KiB
TeX
\section{Comparison with Alternatives}
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\label{sec:comparison}
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% ============================================================
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We compare the FROST+CGGMP21 approach against three deployed alternatives for
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cross-chain custody.
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\begin{table*}[t]
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\centering
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\small
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\begin{tabular}{@{}p{2.8cm}p{2.5cm}p{2.5cm}p{2.5cm}p{2.5cm}@{}}
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\toprule
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\textbf{Property} & \textbf{FROST + CGGMP21} (Teleport) & \textbf{BLS Aggregation} (Wormhole) & \textbf{TSS GG20} (tBTC v2) & \textbf{Multisig} (Gnosis Safe) \\
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\midrule
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Sig. scheme & Schnorr + ECDSA & BLS12-381 & ECDSA (GG20) & ECDSA \\
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On-chain format & Native single sig & Custom verifier & Native single sig & $k$ sigs + contract \\
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Verify cost (EVM) & 3,000 gas & 180,000 gas & 3,000 gas & $3{,}000k$ gas \\
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Chain coverage & 17 families & EVM + custom & secp256k1 only & EVM only \\
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Rounds (signing) & 2 (FROST) / 1+pre (CGGMP) & 1 & 8 & 0 (async) \\
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Identifiable abort & Yes (CGGMP21) & No & No (GG20) & N/A \\
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Key refresh & Yes & No (fixed keys) & Yes & N/A \\
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Bitcoin Taproot & Yes (native) & No & No & No \\
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Ed25519 chains & Yes (native) & No & No & No \\
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Corruption threshold & $t{-}1$ of $n$ & $t{-}1$ of $n$ & $t{-}1$ of $n$ & $k{-}1$ of $n$ \\
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\bottomrule
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\end{tabular}
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\caption{Comparison of threshold/multisig schemes for cross-chain custody.}
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\label{tab:comparison}
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\end{table*}
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\paragraph{BLS Aggregation (Wormhole-style).}
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Wormhole~\cite{wormhole2023} uses BLS12-381 aggregate signatures from a guardian set.
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BLS aggregation provides compact multi-signer proofs but requires a custom on-chain
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verifier (BLS precompile or Solidity implementation) costing 180,000+ gas on EVM.
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BLS12-381 is not natively supported on any major chain except Ethereum (EIP-2537).
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Coverage is limited to chains where the verifier can be deployed.
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\paragraph{TSS GG20 (tBTC v2).}
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tBTC v2~\cite{tbtc2022} uses the GG20 protocol~\cite{gennaro2020} for threshold
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ECDSA. GG20 requires 8 rounds of communication (vs.\ CGGMP21's offline+1 or FROST's
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2 rounds) and lacks identifiable abort---a malicious party can cause signing to fail
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without detection. GG20 covers only secp256k1 chains. No Ed25519 or Taproot support.
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\paragraph{Multisig (Gnosis Safe).}
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On-chain multisig is the simplest approach but has fundamental limitations: (1)~gas
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cost scales linearly in the number of signers $k$; (2)~threshold changes require
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contract transactions; (3)~not available on chains without smart contracts
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(Bitcoin, Stellar); (4)~reveals the threshold structure on-chain.
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\subsection{Security Property Comparison}
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\begin{table}[H]
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\centering
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\small
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\begin{tabular}{@{}lcccc@{}}
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\toprule
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\textbf{Property} & \textbf{Ours} & \textbf{BLS} & \textbf{GG20} & \textbf{Multisig} \\
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\midrule
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EUF-CMA & \checkmark & \checkmark & \checkmark & \checkmark \\
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Id. abort & \checkmark & -- & -- & N/A \\
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Key refresh & \checkmark & -- & \checkmark & -- \\
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Forward sec. & \checkmark & -- & \checkmark & -- \\
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Privacy${}^*$ & \checkmark & -- & \checkmark & -- \\
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UC security & \checkmark${}^\dagger$ & \checkmark & -- & N/A \\
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\bottomrule
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\end{tabular}
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\caption{Security properties. ${}^*$Privacy = threshold structure not revealed on-chain.
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${}^\dagger$CGGMP21 is UC-secure; FROST is proven in the ROM.}
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\label{tab:security}
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\end{table}
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% ============================================================
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