Cryptography Reference
In-Depth Information
n
2
=
n
(
n
−
1)
n
2
−
n
=
1
·
2
2
secret keys that must be generated, stored, managed, and destroyed. This number
grows in the order of
n
2
, and hence the establishment of secret keys is a major
practical problem (and probably the Achilles' heel) for the large-scale deployment
of secret key cryptography. For example, if
n
=1
,
000 entities want to securely
communicate with each other, then there are
1
,
000
2
=
1
,
000
2
−
1
,
000
= 499
,
500
2
secret keys. Even for moderately large
n
, the generation, storage, and management
of so many keys is prohibitively expensive, and the predistribution of the keys is
infeasible.
Things get even more involved when one considers that keys are often used in
dynamic environments, where new entities join and other entities leave at will, and
that it is usually impossible, impractical, or simply too expensive to transmit keys
over secure channels (e.g., by a trusted courier). Consequently, one typically faces
a key establishment problem in computer networks and distributed systems. There
are basically two approaches to address (and hopefully solve) the key establishment
problem in computer networks and distributed systems:
•
The use of a key distribution center (KDC);
•
The use of a key establishment protocol.
A prominent and widely deployed example of a KDC is the Kerberos authen-
tication and key distribution system (see, for example, [4]). Unfortunately, KDCs
have many disadvantages. The most important disadvantage is that each entity must
unconditionally trust the KDC and share a secret master key with it. There are sit-
uations in which this level of trust is neither justified nor can be accepted by the
communicating entities. Consequently, the use of key establishment protocols (that
typically make use of public key cryptography in some way or another) provides a
viable alternative in many situations.
In a simple key establishment protocol, an entity randomly generates a key and
uses a secure channel to transmit it to the communicating peer entity (or entities).
This protocol is simple and straightforward; it is basically what a Web browser does
