of more than two parties). Furthermore, some of these definitions are
not comparable to others (i.e., they neither imply the others nor are
implies by them), and there seems to be no single definition that may
be crowned as the central one.
For example, in Sections 7.1.2 and 7.1.3, we have presented two
alternative definitions of “secure multi-party protocols”, one requiring
an honest majority and the other allowing abort. These definitions are
incomparable and there is no generic reason to prefer one over the other.
Actually, as mentioned in Section 7.1.2, one could formulate a natural
definition that implies both definitions (i.e., waiving the bound on the
number of dishonest parties in Definition 7.1). Indeed, the resulting
definition is free of the annoying restrictions that were introduced in
each of the two aforementioned definitions; the “only” problem with
the resulting definition is that it cannot be satisfied (in general). Thus,
for the first time in this primer, we have reached a situation in which a
natural (and general) definition cannot be satisfied, and we are forced
to choose between two weaker alternatives, where each of these alter-
natives carries fundamental disadvantages.
In general, Section 7 carries a stronger flavor of compromise (i.e.,
recognizing inherent limitations and settling for a restricted meaningful
goal) than previous sections. In contrast to the impression given in other
parts of this primer, it is now obvious that we cannot get all that we
may want (see Section 7.4). Instead, we should study the alternatives,
and go for the one that best suits our real needs.
Indeed, as stated in Section 1.1, the fact that we can define a crypto-
graphic goal does not mean that we can satisfy it as defined. In case
we cannot satisfy the initial definition, we should search for relaxations
that can be satisfied. These relaxations should be defined in a clear
manner so that it would be obvious what they achieve (and what they
fail to achieve). Doing so will allow a sound choice of the relaxation to
be used in a specific application. This seems to be a good point to end
the current primer.
A good compromise is one in which
the most important interests
of all parties are satisfied.