Cryptographic Systems - Contemporary Cryptography - page 42

• If the entities have a trusted party at their disposal, then there is a trivial

solution for the problem: all entities securely transmit their input values to the
trusted party, and the trusted party, in turn, evaluates the function and provides
the result to all entities (it goes without saying that all communications must
take place over secure channels).

• If, however, the entities have no trusted party at their disposal, then the

situation is more involved. In this case, it is not at all obvious that the problem
can be solved at all.

In the second case, we are in the realm of secure multiparty computation.
We ask for cryptographic protocols that can be used by the entities to evaluate a
function and to effectively simulate a trusted party. Such protocols can be found
and have many (potential) applications, such as electronic voting and mental game
playing (i.e., playing a game over a communication network). In Chapter 18, we
briefly touch on secure multiparty computation and the major results that have been
found in theory.

2.4 FINAL REMARKS

In this chapter, we briefly introduced and provided some preliminary definitions
for the most important representatives of the three major classes of cryptosystems
distinguished in this topic (i.e., unkeyed cryptosystems, secret key cryptosystems,
and public key cryptosystems). We want to note (again) that this classification
scheme is somewhat arbitrary, and that other classification schemes may be used
instead.
In either case, the cryptosystems that are preliminarily defined in this chapter
are refined, more precisely defined (in a mathematical sense), discussed, and put into
perspective in the later parts of the topic. For all of these systems, we also elaborate
on the notion of security and try to find appropriate definitions and evaluation
criteria for secure systems. In fact, a major theme in contemporary cryptography
is to better understand and formally express the notion of security, and to prove
that a particular cryptosystem is secure in exactly this sense. In many cases, the
cryptographic community has been surprisingly successful in doing so. This is what
the rest of this topic is basically all about. We have to begin with some mathematical
fundamentals first.

References

[1] Luby, M., Pseudorandomness and Cryptographic Applications . Princeton Computer Science

Notes, Princeton, NJ, 1996.