MPC signing requires t+1 nodes instead of t nodes when threshold = t

[clr34m3r]

While testing the implementation of mpcium, I noticed a behavior that seems inconsistent with the expected fault-tolerance guarantees of a threshold MPC scheme.

In a standard MPC / threshold signature model, when the threshold is set to t, the system should be able to:

• Remain functional as long as any t out of n nodes are available
• Successfully complete signing operations with t participating nodes
• Tolerate up to n − t node failures or unavailability

However, in the current mpcium implementation, signing only succeeds when at least t + 1 nodes are ready and participating in the protocol.
This effectively means:

• The real operational threshold is t + 1, not t
• The system tolerates fewer node failures than expected

Is the t + 1 requirement an intentional design decision?

[anhthii]

hi @clr34m3r thanks for raising the issues

Yes, the t + 1 requirement is intentional, and the assumptions in that message are not aligned with how standard threshold MPC / TSS schemes are defined.

In an (n, t) threshold signature scheme:

t is the security threshold, meaning the system remains secure even if up to t nodes are malicious or compromised.

Signing requires at least t + 1 participating nodes. This is the minimum quorum needed for a valid threshold signature.

As a result, the system can tolerate up to n − ( t + 1 ) unavailable nodes while still being able to sign.

https://github.com/bnb-chain/tss-lib