Cryptography Reference
In-Depth Information
Chapter 7
Introduction to Public-Key Cryptography:
The Diffie-Hellman Protocol
In this chapter, we present an introduction to the ideas underlying public-key
cryptography and we illustrate some of them with the very first public-key pro-
tocol. This protocol is the Diffie-Hellman key agreement, which was proposed in
[67] and heralded the birth of public-key cryptography.
7.1 From Private-Key to Public-Key Cryptography
The private-key encryption schemes we have studied in preceding chapters have
some drawbacks when used in the context of modern communication networks. The
main inconvenience is that the communicating parties, Alice and Bob, must share a
secret key and for this they need a secure channel. This channel may adopt different
formats and it might be, for example, a physical meeting between Alice and Bob or a
trusted courier. When cryptography was the domain of government agencies and the
military—as happened until the last quarter of the twentieth century—this was not a
big problem because these organizations had the capacity to use these channels. But
for average users of modern communication systems, secure channels are not readily
available—in fact, it may be said that these channels are notoriously scarce. This is
the problem Alice and Bob face if, for example, they live in different continents and
want to communicate by e-mail. This key exchange problem becomes even more
important if we consider a large group of people who want to communicate through
an open network like the Internet. If the number of users of the communication
network is n and any two of them exchange a secret key for private communication,
then n
(
n
1
)/
2 keys must be exchanged and securely stored, and each user must
keep n
1 keys. If one takes into account that, for security reasons, the keys should
be renewed periodically, it is clear that both the key distribution and key management
problems soon become intractable.
These problems may be alleviated by means of a key center that acts as a sort
of intermediary between users. In its simplest incarnation, the key center works as
 
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