Three-Party Security Issue

[Julen Bernabé]

Hi SCALE-MAMBA Community,

I'm working on an MPC use case where two parties want to perform some computations over their sensitive inputs. In this specific use case, there's an orchestrator who decides when the computations start. In summary, we have the set of players P={1,2,O} where O is the orchestrator.

Thus, we have a 3PC where one of the parties participates but does not give any input. Assuming the worst case, let's suppose this orchestrator is controlled by one of the parties. I'm worried about data leakages that may arise from this use case using SCALE-MAMBA:

• Shamir Secret Sharing: I assume using this approach is totally insecure, since the access structure derived from the threshold results in sets {{1,O},{2,O}} being qualified.
• Replicated Sharing/Q2-MSP Sharing: In this case, we can make the above sets unqualified, but the resulting access structure is not Q2... Is there something I'm skipping here?
• Full-Threshold: I assume, without entering in the details, that this approach would be secure, but I'm not sure...

Therefore, in case the orchestrator is controlled by one of the parties, the only possible solution is to use the Full-Threshold approach, am I right?

In case the orchestrator is controlled by a third party that is totally independent from the first two, is there any chance for the Shamir Secret Sharing approach to be secure? What happens if a party does not give inputs, does that turn the protocol insecure?

Thanks beforehand for your attention,

Julen

[Nigel Smart]

Indeed if the orchestrator is possibly controlled by one of the parties then you
need Full Threshold.  If independent then you can go for Shamir

Nigel

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