what's the reason to using a three-party protocol

[libratiger]

In this section we describe our protocols for performing encrypted computations using the three-party replicated secret sharing scheme.

https://github.com/tf-encrypted/moose-whitepaper

is there any reason why do not using a four-party or other party protocol?

[rdragos]

We had to start from somewhere so we picked the simplest one.

Of course it is possible to add support for other protocols but at the time we chose to spend effort into developing more ops for the replicated case in order to be more robust.