Main content

## Computer science

### Unit 2: Lesson 4

Modern cryptography- The fundamental theorem of arithmetic
- Public key cryptography: What is it?
- The discrete logarithm problem
- Diffie-hellman key exchange
- RSA encryption: Step 1
- RSA encryption: Step 2
- RSA encryption: Step 3
- Time Complexity (Exploration)
- Euler's totient function
- Euler Totient Exploration
- RSA encryption: Step 4
- What should we learn next?

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# Public key cryptography: What is it?

Why do we need public key cryptography? Created by Brit Cruise.

## Video transcript

Brit: After World War 2,
with most of Europe in ruins, tension grew between the
Soviet Union and the United States. It was clear that the
next global superpower required the ability to both
launch and successively defend nuclear attacks from
intercontinental ballistic missiles. In North America, the most vulnerable
point of attack was over the North Pole. So in 1958, a joint effort between
United States and Canada was established, known as NORAD, or North American Aerospace
Defense Command. An important line of defense was the
semi-automatic ground environment. It was an automated system of
over 100 long-distance radars scattered across North America. They were connected to
computerized radar stations that transmitted tracking data using
telephone lines or radio waves. All of this radar information was
fed into a primary warning center buried a mile deep inside
Cheyenne Mountain in Colorado. This application of machine
to machine communication allowed operators to make
split-second decisions using information transmitted and
processed automatically by computers. This idea of being online was
quickly adapted and advanced by universities in the following years as they understood the potential
of computer networking. Man: The thing that makes the computer communication network
special, is that it puts the workers -- that'd be the team members who
are geographically distributed -- in touch not only with one another, but with the information base
with which they work all the time. And this is obviously going to make a
tremendous difference in how we plan, organize, and execute almost everything
of any intellectual consequence. If we get into a mode in which
everything is handled electronically, and your only identification is some little plastic thing
you stick into the machinery, then I can imagine that they
want to get that settled up with your bank account just right now,
and put it through all the checks, and that would require a network. Brit: Money transfers are just one of
a growing number of applications which required encryption
to remain secure; and as the internet grew to
encompass millions around the world, a new problem emerged. At the time, encryption
required two parties to first share a secret random
number, known as a key. So how could two people
who have never met agree on a secret shared key without letting Eve,
who is always listening, also obtain a copy? In 1976, Whitfield Diffie
& Martin Hellman devised an amazing trick to do this. First, let's explore how this
trick is done using colors. How could Alice and Bob agree on a
secret color without Eve finding it out? The trick is based on two facts: one, it's easy to mix two colors
together to make a third color; and two, given a mixed color,
it's hard to reverse it in order to find the
exact original colors. This is the basis for a lock: easy in one direction,
hard in the reverse direction. This is known as a one-way function. Now, the solution works as follows: First, they agree publicly on
a starting color, say yellow. Next, Alice and Bob both
randomly select private colors, and mix them into the public yellow
in order to disguise their private colors. Now, Alice keeps her private color
and sends her mixture to Bob, and Bob keeps his private color
and sends his mixture to Alice. Now, the heart of the trick: Alice and Bob add their private colors
to the other person's mixture and arrive at a shared secret color. Notice how Eve is unable to
determine this exact color, since she needs one of
their private colors to do so. And that is the trick. Now, to do this with numbers,
we need a numerical procedure which is easy in one direction
and hard in the other.