Difference to Multi-Signatures

What is the difference between TSS and Multi Signatures?

The main difference between Threshold Signature Schemes (TSS) and Multi-Signatures (MS) lies in their approach to generating signatures. In TSS, the signature is created by combining vault shares using Zero-Knowledge Proofs, ensuring that no single private key is ever constructed. In contrast, MS involves multiple private keys, each contributing to the creation of the final signature.

Visualization Threshold Signatures

Threshold Signatures

Visualization Multi-Signatures

Multi-Signatures

Increasing the inconvenience of Multi-Signatures (MS) is the fact that lost keys cannot be re-shared, and funds often need to be migrated to maintain security, leading to lower redundancy.

Here is a comparison of different factors for TSS and MS:

Factors	Threshold Signature Scheme	Multi-Signature
Private Key Storage	No private key is constructed; uses vault shares and Zero-Knowledge Proofs	Parties having multiple private keys
On-Chain Footprint	One Single Signature signing a Transaction on-chain	Multiple Signatures signing one Transaction; visible on-chain
Redundancy	High redundancy; lost shares can be re-shared and reconfigured	Low redundancy; lost keys require fund migration
Compatibility	Multi-Chain: ECDSA and EDDSA Support	Single Chain Support
Flexibility	Can adjust signing thresholds and replace lost devices	Fixed once created; each party having one private key
Adding participants	✔	❌

This comparison shows that flexibility and security prevail in TSS over MS, making it a better application for managing digital assets.