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tion, which essentially asserts that there is no way to prevent a party
from prematurely suspending the execution (46). On the other hand,
secure multi-party computation with dishonest majority is possible if
premature suspension of the execution is not considered a breach of
security (cf. Section 7.1.3).
7.1.3
Another example: Two-party protocols allowing abort
In light of the last paragraph, we now consider multi-party computa-
tions in which premature suspension of the execution is not considered
a breach of security. For concreteness, we focus here on the special case
of two-party computations. 3
Intuitively, in any two-party protocol, each party may suspend the
execution at any point in time, and furthermore it may do so as soon
as it learns the desired output. Thus, in case the output of each parties
depends on both inputs, it is always possible for one of the parties to
obtain the desired output while preventing the other party from fully
determining its own output. The same phenomenon occurs even in case
the two parties just wish to generate a common random value. Thus,
when considering active adversaries in the two-party setting, we do
not consider such premature suspension of the execution a breach of
security. Consequently, we consider an ideal model where each of the
two parties may “shut-down” the trusted (third) party at any point
in time. In particular, this may happen after the trusted party has
supplied the outcome of the computation to one party but before it
has supplied it to the other. That is, an execution in the ideal model
proceeds as follows:
(1) Each party sends its input to the trusted party, where the
dishonest party may replace its input or send no input at all
(which can be treated as sending a default value).
(2) Upon receiving inputs from both parties, the trusted party
determines the corresponding outputs, and sends the first
output to the first party.
3 As in Section 7.1.2, we consider a non-adaptive, active, computationally-bounded adver-
sary.
 
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