Also called Schnorr MPC Signature

(2,3) Threshold Signature:

3 people, each one holding 1 secret share.

Any 2 of them can communicate with each other and generate a valid signature, without revealing its secret share.

Compatible with single-party signature. You cannot find differences between their output signatures.

Schnorr Signature

Schnorr & ZK

Schnorr ∑-protocol is easier to understand

The Schnorr signature scheme is obtained by making the Schnorr ∑-protocol non-interactive using the Fiat-Shamir heuristic, where the challenge c is derived from the message m and the commitment r using a hash function.

Secret Sharing

Secret Sharing is a common component of Threshold Signature

In $$(t,n)$$ threshold signature, the first step is to divide the secret key $$s$$ into $$n $$ shares, any $$t$$shares can recover the secret key

Shamir Secret Sharing (SSS)

Dealer:

• Generate $$t-1$$ random coefficients $$a_1, ..., a_{t-1} $$
• t = 2
• a1 = 2
• Construct a degree $$t-1$$ polynomicals $$f(x) = s + \sum^{t-1}_{i=1}{a_ix^i}$$