Cryptography Reference
In-Depth Information
Public-Key Encryption
5
In this chapter we take our first detailed look at public-key cryptography. As for
symmetric cryptography, our first chapter on this subject will primarily focus
on using public-key cryptography for encryption. Throughout this discussion we
will tend to refer to public-key 'cryptosystems'. This is because describing how
to conduct public-key encryption involves a discussion of how to generate the
necessary keys as well as how to conduct the encryption and decryption processes.
In this chapter we will assume, by default, that a public-key cryptosystem is used
to provide encryption. In later chapters we sometimes choose to make this more
explicit by referring to
public-key encryption schemes
.
We first consider the motivation behind the concept of public-key cryptogra-
phy and identify some of the problems that need to be solved before it can be used
effectively. We will then turn our attention to two of the best-known public-key
cryptosystems. Note that in contrast to our treatment of symmetric encryption,
we will make an attempt to explain the mathematical details behind these two
public-key cryptosystems. There are two main reasons for this:
1. Public-key encryption is less intuitive than symmetric key encryption, hence
it merits several proofs of concept. Seeing, and hopefully understanding, is
believing!
2. The algorithms used in public-key encryption are easier to describe than those
used in symmetric encryption since they rely on simple mathematical ideas and
not relatively complex engineering.
However, it is perfectly acceptable to skip over the mathematical details of these
public-key cryptosystems without losing track of the main issues. For those who
wish for more grounding in these basic mathematical ideas, we have included
background material in the Mathematics Appendix.
At the end of this chapter you should be able to:
• Explain the basic principles behind public-key cryptography.
• Recognise the fundamental problems that need to be solved before public-
key cryptography can be used effectively.
• Describe a simple version of the RSA cryptosystem.
