Implementing-cryptography-using-python

120 Chapter 4 ■ Cryptographic Math and Frequency Analysis
Frequency Analysis
The primary focus of this section is to teach the computer to recognize when
a set of letters matches the frequency distribution of plaintext English. You
can apply the information in this section in a number of different ways. The
ultimate goal is to give you the tools you need to be able to crack a number of
classical ciphers.
Frequency analysis is the study of the frequency of letters or the combination
of letters. It is based on the fact that, within any written language, certain letters
and combinations of letters will occur with varying frequencies. When you
examine the frequency of letters used in the English language, you find that the
letters E, T, A, and O are the most common, while Z, Q, and X are found with
much less frequency. Examine Figure 4.5 to see the occurrence of each letter.
Figure 4.5: FA.py
We will also find higher frequency of letter combinations such as TH, ER, ON,
and AN. These combinations are known as bigrams or digraphs. There are also
common pairs of repeating letters such as SS, EE, TT, and FF. When you encrypt
English plaintext into ciphertext using many historical ciphers, these same
properties will be preserved and can be exploited in a ciphertext-only attack.
As you will recall, historical substitution ciphers replace each letter in the
plaintext with an alternate letter. If you use the Caesar cipher to encrypt the
letter E with a key of 3, then each occurrence of E will now be H. If you have
enough text to determine that H is the letter with the most frequency, then you
may determine that the key is the difference between the letters H and E. This