Cryptography Reference
In-Depth Information
Chapter 2
Cryptographic Systems
As mentioned in Section 1.2.1, there are three major classes of cryptographic sys-
tems: unkeyed cryptosystems, secret key cryptosystems, and public key cryptosys-
tems. In this chapter, we briefly introduce and provide some preliminary definitions
for the most important representatives of these classes in Sections 2.1-2.3 (the def-
initions are partly revised and refined in later parts of the topic). We conclude with
some final remarks in Section 2.4.
2.1
UNKEYED CRYPTOSYSTEMS
According to Definition 1.5, unkeyed cryptosystems use no secret parameter. Ex-
amples include one-way functions, cryptographic hash functions, and random bit
generators. Let us have a preliminary look at these systems.
2.1.1
One-Way Functions
The notion of a one-way function plays a central role in contemporary cryptography.
Informally speaking, a function f : X
Y is one way if it is easy to compute
but hard to invert. In accordance with the terminology used in complexity theory
(see Chapter 6), the term easy means that the computation can be done efficiently,
whereas the term hard means that the computation is not known to be feasible in an
efficient way (i.e., no efficient algorithm to do the computation is known to exist). 1
Consequently, one can define a one-way function as suggested in Definition 2.1 and
illustrated in Figure 2.1.
1
Note that it is not impossible that such an algorithm exists; it is just not known.
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