path: root/DKG-Protocol.md

DEXON DKG Protocol
===========================
### Parameter
* λ = One gossip time
* Signature = [BLS](https://en.wikipedia.org/wiki/Boneh%E2%80%93Lynn%E2%80%93Shacham)
* Curve = CurveFp382_2
* t = <img src="https://latex.codecogs.com/svg.latex?\inline%20\frac{1}{3}n+1" />

Phase 1 ID Registration 
-------
### @ T < 0

Each validator register its ID with stack.

Phase 2 Secret Key Share Exchange
-------
### @ T = 0
Each validator `i` generates `n` (`n` = # of ID registered in phase 1) secret key shares (`SK_i,0, SK_i,1, ..., SK_i,n`) of order `t` and the secret key share is sent to the corresponding validator (`SK_i,j` is sent to validator `j`) via a secure channel.

Each validator `i` broadcast the master public key (`MPK_i`) of order `t` associated with the secret key shares.

Each validator `i` broadcast public key shares (`PK_i,0, PK_i,1, ..., PK_i,n`) associated with secret key shares.

Phase 3 Complaint
-------
### @ T = 2λ
Each validator `i` verify if the secret key share `SK_i,j` is associated with the public key share of validator `j` `PK_i,j`. If the verification fails, `i` broadcast complaint of `j`, `CMP_i,j`.

Phase 4 Disqualify Byzantine Node
-------
### @ T = (2λ, 4λ)
If there are more than `t` complaints to validator `j` (<img src="https://latex.codecogs.com/svg.latex?\inline%20\sum_{i}%20CMP_{i,j}%20>%20t" /> (`i` : for all validator `i`)), then `j` is marked as **Disqualified**.

Each validator `i` determines the combined secret key, <img src="https://latex.codecogs.com/svg.latex?\inline%20CSK_{i}%20=%20\sum_{k}%20SK_{k,i}" /> (`k`: validator `k` is not marked as **Disqualified**)

Each validator `i` determines the combined public key, <img src="https://latex.codecogs.com/svg.latex?\inline%20CPK_{j}%20=%20\sum_{k}%20MPK_{k}" /> (`k`: validator `k` is not marked as **Disqualified**)

Phase 5 Sign with CSK
-------
### @ T = 4λ
Each validator `i` sign the message with `CSK_i` and broadcast the signature, `Sign_i`.

Phase 6 TSIG
-------
### @ T = (4λ, +inf)
Verify `Sign_i` with `CPK_i`.

Collect more than `t` valid `Sign_i` and recover TSIG.