Problem with understanding Multi-party security circuit for secure stable matching I am reading the following paper:
MPCircuits: Optimized Circuit Generation for Secure Multi-Party Computation

Paper Link

I have following question:

We have two groups shown in the circuit. Why we call it a multi-party circuit?

Paper provides a comparison of its multi-part technique with the old 2 part based technique:


  In secure stable matching, the match list is computed while keeping
  the  preference lists private to their respective owners. This problem
  has  been studied in the recent literature [21], [22] where the secure
  stable matching problem is reduced to a two-party secure computation 
  scenario. Each individual XOR shares her preference list and sends it 
  to two non-colluding servers who perform the secure computation. 
  However, stable matching is inherently a multi-party problem and the 
  assumption of two non-colluding servers may not be feasible in 
  practice. To the best of our knowledge, we provide the first solution 
  for multi-party secure stable matching.


The attached figure shows only how to input the preference list of group#1 and group#2. How can we perform n*n computation using the figure?
 Somebody please guide me. Zulfi.
Stable matching involves finding a matching between two groups of people (group 1, say males, and group 2, say females).  Those are the groups that is referring to.