Implementing-cryptography-using-python

138 Chapter 4 ■ Cryptographic Math and Frequency Analysis
Summary
This chapter was fairly heavy on the important mathematical concepts you
need to break classical ciphers. You may find yourself referring to this chapter
several times as you progress through the remaining chapters. Before moving
on to the next chapter, make sure you have a pretty good understanding of
modular arithmetic and how to find the inverse. In addition, you should have
an understanding of basic group theory, the Chinese remainder theorem, and
solving linear equations. A number of Python libraries are available that will
simplify a great deal of the concepts offered in this chapter. It is vital that you
remember the importance of using cryptographically secure pseudorandom
generators and also understand how to determine the random number generation
that is offered using C’s rand() function. Frequency analysis will be
your greatest ally. As you generate decryption keys, knowing how frequency
analysis works will help you decrypt many of these ciphers without knowing
the keys or key lengths.
We will be continuing our exploration of cryptanalysis as you progress through
the remaining chapters, but you should have a good understanding of how to
decrypt a wide variety of cryptographic schemes.