Implementing-cryptography-using-python

224 Chapter 8 ■ Cryptographic Applications and PKI
something had to be done, which led to the development of the holy grail of
cryptography. In this chapter, you will learn about a secret code so ingenious
that it would change the way we communicate forever. Through this chapter,
you gain cryptographic knowledge as you:
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Gain an understanding of the importance of PKI
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Learn how to implement a PKI solution in Python
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Gain an understanding of RSA
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Learn how to implement ElGamal
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Gain an understanding of Elliptic Curve Cryptography
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Learn how to implement a key exchange using Diffie-Hellman
The Public-Key Transformation
In 1975, Martin Hellman, Whitfield Diffie, and Ralph Merkle were working in
the electrical engineering department at Stanford University; unlike most cryptographers,
they worked outside the classified world of military intelligence. The
team proposed that, instead of the sender being responsible for encryption, the
receiver of the message would be responsible. The proposal asks the receiver for
their padlock to lock up the sender’s message. The system works because the
participants are exchanging padlocks and not the keys themselves. The keys are
always with the receiver; this mitigates the keys falling into the wrong hands.
Since it is not practical to send physical padlocks, the team had to invent a way
to create a mathematical padlock; these are often referred to as trapdoors. The
mathematical padlock had to be easy to lock but difficult to unlock without the
key. Developing the mathematical padlock was not a trivial process since most
operations are easy to do one way and easy to reverse. An example is taking a
number and then doubling it; for this example, if x = 20, and y = 2 * x, then y =
40. To reverse the process, it is easy to find half of y: x = y/2. This is an example
of two-way operation. To find the perfect mathematical padlock, it is necessary
to find a one-way operation. Multiplication is the perfect tool. If you are given
two four-digit numbers and asked to multiply the two numbers together, you
can easily complete the task. However, if you are given the product and asked
to work backward, that is a much harder problem to solve. To illustrate this
example, let’s assume you start with the number 3,261,611. Can you provide
the two numbers used to produce the number (aka factoring)? Where would
you start?
Multiplying two large integers together creates a mathematical lock, but it is
also a lock without a key. As such, it is an operation that is irreversible unless
you have the mathematical equivalent of a key. Enter Clifford Cocks; Cocks