Cryptography Reference
In-Depth Information
Chapter 5
Information Theory
As mentioned in Section 1.3, Claude E. Shannon developed a mathematical theory
of communication [1] and a related communication theory of secrecy systems [2]
that started a new branch of research commonly referred to as
information theory
.
Information theory has had (and continues to have) a deep impact on contemporary
cryptography.
In this chapter, we briefly overview and discuss the basic principles and results
of information theory as far as they are relevant for contemporary cryptography.
More specifically, we introduce the topic in Section 5.1, elaborate on the entropy
to measure the uncertainty of information in Section 5.2, address the redundancy
of languages in Section 5.3, introduce the key equivocation and unicity distance
in Section 5.4, and conclude with some final remarks in Section 5.5. Again, this
chapter is intentionally kept short; further information can be found in any topic
about information theory (e.g., [3-5]).
5.1
INTRODUCTION
Information theory is concerned with the analysis of a
communication system
that
has traditionally been represented by a block diagram as illustrated in Figure 5.1.
The aim of the communication system is to communicate or transfer information
(i.e., messages) from a source (on the left side) to a destination (on the right side).
The following entities are involved in one way or another:
•
The
source
is a person or machine that generates the messages to be commu-
nicated or transferred.
•
The
encoder
associates with each message an object that is suitable for trans-
mission over the channel. In digital communications, the object is typically
