  In secure multi-party computation $n$ parties jointly evaluate an $n$-variate
function $f$ in the presence of an adversary which can corrupt up till $t$
parties. Almost all the works that have appeared in the literature so far
assume the presence of authenticated channels between the parties. This
assumption is far from realistic. Two directions of research have been borne
from relaxing this (strong) assumption: (a) The adversary is virtually
omnipotent and can control all the communication channels in the network, (b)
Only a partially connected topology of authenticated channels is guaranteed and
adversary controls a subset of the communication channels in the network.
  This work introduces a new setting for (unconditional) secure multiparty
computation problem which is an interesting intermediate model with respect to
the above well studied models from the literature (by sharing a salient feature
from both the above models). We consider the problem of (unconditional) secure
multi-party computation when 'some' of the communication channels connecting
the parties can be corrupted passively as well as actively. For this setting,
some honest parties may be connected to several other honest parties via
corrupted channels and may not be able to authentically communicate with them.
Such parties may not be assured the canonical guarantees of correctness or
privacy. We present refined definitions of security for this new intermediate
model of unconditional multiparty computation. We show how to adapt protocols
for (Unconditional) secure multiparty computation to realize the definitions
and also argue the tightness of the results achieved by us.
