Implementing-cryptography-using-python

Chapter 8 ■ Cryptographic Applications and PKI 245
Your results should look like those shown in Figure 8.8.
Figure 8.8: Diffie-Hellman exchange example
Summary
In this chapter, you were able to expand on your knowledge of working with a
public-key infrastructure using Python. The biggest secrets in our government
and business entities are largely protected by two simple mathematical equations:
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C = M e (mod N)
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C 1/e mod (p – 1) (q – 1) mod N = M
These equations provide the basis of creating very large keys that are easy
to generate but difficult to crack, essentially creating mathematical locks or
trapdoors.
After gaining an understanding of how PKI works, we then explored how to
implement ElGamal, which is a cryptosystem based on the difficulty of finding
a discrete logarithm in a cyclic group.
The use of large keys in cryptography could have limitations as the world
moves to smaller mobile devices. You also learned about the elliptic curve cryptography
encryption system, which provides an alternative and more efficient
type of public-key cryptography. The use of ECC is critical to how we implement
key exchanges using the Diffie-Hellman algorithms.
In the next chapter, you will create a chat application that will incorporate
many of the recipes and styles you have learned in this book.