This scenario is one that can take place entirely offline
Hi @steven_intu I am not sure something like this would be possible using the current protocol, which is inherently interactive. Moreover, you cannot compute ECDSA sigs only with linear operations. So if you use a linear sharing schemes like in this protocol, some amount of interaction and preprocessing will always be needed.
A 3(t) of 4(n) scheme being the first requirement.
As stated in the paper, the scheme only supports f<n/3 byzantine corruptions. Maybe you can have a look at this thread for a similar discussions. The reason the IC integrated this protocol is that it relies on the same assumptions already made by the IC protocol, while giving strong guarantees in terms of security and availability. It seems that your assumptions and setup may be quite different, and that you would be willing to relax some of these requirements. There are many threshold ECDSA protocols in the dishonest majority settings where you could get higher thresholds. Maybe these would be a better fit for your use case. A starting point could be the related work section of the paper.