Threshold Schemes in Blockchains and HSMs

Bitcoin and Ethereum support on-chain multi-signature scripts (P2MS/P2SH/multisig in Solidity). These require t-of-n public keys to co-sign a transaction, verified by the blockchain. The structure is public and transparent: anyone can see that the address requires multiple signers. Threshold ECDSA produces a standard single-key address and a standard single signature, making threshold structure completely invisible on-chain.

Threshold ECDSA advantages over on-chain multi-sig: a single transaction signature (lower gas fees), no multi-sig policy visible on-chain (privacy), compatible with any blockchain that uses ECDSA (including chains without native multi-sig support), and key rotation without changing the blockchain address (since the public key stays the same after a key refresh). These advantages make threshold ECDSA the preferred approach for institutional custody.