FROST [1] is the most recent threshold signature scheme that sacrifices robustness for reducing communication complexity. We consider braidpool’s communication model and our requirements from a threshold signature scheme (TSS). We argue that we braidpool will benefit from FROST’s signing phase without a signature aggregator and that braidpool should use Pedersen’s DKG for robust distributed key generation (DKG). Both of these are suggestions from the FROST paper.

Braidpool’s Communication Channels

In braidpool, a gossip based reliable P2P broadcast protocol is available for exchange of shares between miners. This broadcast channel is used for both reliably broadcasting messages and privately sending messages to individual miners. Private unicast works by encrypting messages to the receiver. Just as in LN, the miners in braidpool identify themselves with a public key. This public key is used to encrypt a private message for a receiver.

Rounds of Communication

We leave out any timeliness constraints out of this discussion and will consider them in another post. For now, we assume a round is decided upon by the miners using synchronised clocks. In a follow up post we will remove this assumption.

DKG and TSS Requirements for Braidpool

In braidpool we run DKG and a TSS when creating new blocks. The DKG and TSS outcomes are to be used as:

  1. A new public key - The pool uses this public key for the creating coinbase transactions. This is the public key which will be spent using a TSS execution. We call this key the pool key.
  2. Signing UHPO transactions - Miners payouts are tracked using Unspent Hasher Payouts (UHPO) [2, 3], which are taproot transactions with time locks. The UHPO transaction is used to pay out all miners who have earned rewards from previous braidpool blocks. Each UHPO spends the coinbase transaction and the UHPO transaction from the last braidpool block that was confirmed as a bitcoin block. We need to run the signing phase matching the DKG that was run to generate the previous coinbase. We sign the UHPO transaction with this block’s pool key.

In Braidpool we generate a pool key that is later used to sign transactions. We also sign a transaction with an older pool key. Therefore, we require that the protocol be robust to handle relatively large delays between the generation of pool key and its use for signing during which time the set of active miners can change.

Consider the situation where at time $T_1$ the set of miners $M_1$ generate a pool key, $PK_{M_1}$. Once the set of miners changes, say to $M_2$, a new round of DKG is run to generate $PK_{M_2}$. The new UHPO transaction spends the previous UHPO transaction as well as the previous block’s coinbase. To handle this, the miners run a DKG to generate the new pool key and run the signing protocol with the previous cohort of miners to spend the previous coinbase transaction and the previous UHPO transaction.

This shows that our choice of DKG and TSS protocols should support:

  1. Robust signing phase - This is required to handle the situation where the set of miners participating in two consecutive bitcoin blocks change. We will run the signing phase of the TSS scheme with the previous set of miners.
    1. FROST’s efficient signing protocol helps us here. By running the DKG and the preprocessing phase to generate a single set of nonces at the same time. The signing phase will then run with the miners set $M_{signing} = M_1 \cap M_2$ as long $|M_{signing}| > 2/3 * |M_1| + 1$.
  2. Robust DKG phase - The DKG protocol has to finish in the presence of misbehaving nodes that can block braidpool’s progress. That is we need the DKG protocol to be robust. The FROST paper chooses a non-robust DKG because in their use case the participants will need figure out the problem out of band and restart the DKG. We instead need the DKG to proceed even under an attack by a participant. We propose using Pedersen’s DKG. The FROST paper makes the same recommendation to implement a robust DKG protocol.

Signature Aggregator

FROST also proposes using a Signature Aggregator elected from the set of participating signers. They suggest that applications that don’t want this centralisation pressure should use a broadcast channel to aggregate the final signature on all participating signers. This results in an increased communication cost and we accept this cost to avoid a bad actor being elected as the signature aggregator and potentially disrupting the workings of Braidpool.

Since braidpool has a broadcast channel available, we will use the broadcast approach to get the threshold signature on all miners.


We have made the following decisions when running FROST threshold signature scheme:

  1. DKG - Use Pedersen’s DKG
  2. Signature - Use FROST scheme without the signature aggregator


[2] Braidpool specs
[3] Generating pool key and blocks to mine