A Brief Introduction to Threshold Signature

Core Technicals
1

Threshold signatures are digital signatures which require a subset of signers among the whole group to produce signatures on behalf of the group. The number of signers in the subset should reach a threshold, for example, a ( t,n )-threshold signature scheme is a digital signature scheme where any t or more signers of a group of n signers can produce signatures on behalf of the group. And a threshold signature does not reveal the actual group members that have cooperated to produce it.

The below links provides more details of principles of threshold signature scheme as well as comparisons with other algorithms.
https://medium.com/blockchain-at-berkeley/alternative-signatures-schemes-14a563d9d562

The following links provides its usages and designs.
https://gitlab.com/polychainlabs/threshold-ed25519
https://github.com/KZen-networks/multi-party-eddsa/wiki/Aggregated-Ed25519-Signatures
https://research.codechain.io/t/bls-signatures-in-tendermint/27

2

What are the pros and cons of threshold signature vs a list of signatures?

3

For Multisig scheme, it requires independent keys for each participant and each signature to be checked individually. As a result, more processing power is needed. Besides, in Multisig, the number of signers are exposed on the blockchain which might harm privacy.

In threshold signature scheme, it requires a minimum number of participants to contribute a share of the signature in order to produce a single overall valid signature. This spares the effort for each participant to keep a private key and the signature will look like a single one without multiple checks. In other words, this also hides the details for signers which enhances the privacy. Threshold signature also provides more flexibility. It is easy to add an arbitrary number of participants to the group.