Why do authors say conflicting things regarding leak-free stages in their paper? In this paper the last sentence of the first paragraph in the abstract states: 


  We assume a (necessary) “leak-free” preprocessing stage.


But then later on in section 1.4 they say


  Another interesting open question is to construct a leakage- resilient
  MPC protocol without assuming any leak-free stages,


Why do they say the leak-free stage is necessary but then later on they say it's an interesting open question ? When they say it's necessary doesn't that imply there is no open question (i.e. not debatable) ?

Is there any research done on leak-free stageS?
I think they are saying assuming leak free is necessary to prove security for their protocol, but it would be really cool (thus an open problem) to design a protocol that can tolerate leaks in any stage.