# Lecture 20: Cryptography

Taught by ArsDigita
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Part of video series
Lesson Summary:

In this math video lesson, viewers will learn about cryptography and its connection to number theory. The lesson starts with an introduction to Euclid's algorithm and greatest common divisors, and goes on to discuss the basics of number theory, including arithmetic modulo other numbers. The main focus of the lesson is on Fermat's Little Theorem, a theorem in number theory that is essential to public key cryptography systems. The lesson also briefly touches upon the history of cryptography and how it has evolved to become virtually unbreakable.

Lesson Description:

Learn about cryptography, an application of Discrete Math and combinatorics.

• What is cryptography and what does it have to do with Euclid's Algorithm and modulus?
• How do public key cryptography systems work?
• In what ways did people encode and decode things in the past?
• How does encoding and decoding have to do with factoring large numbers into its primes?
• What is Fermat's Little Theorem and how does it relate to cryptography?
• What is the proof of Fermat's Little Theorem?
• How can you encode or decode a message if it was encoded using a key word, and each letter of the message was encoded using a letter of the word as the encoding shift?
• What is an example of a function that is difficult to find an inverse to go backward with?
• How is it possible that a person could know how a message was encoded, but be unable to decode it?
• What is the math behind secure online credit card transactions?
• What is public encoding and private decoding?
• Why is mathematically decoding a message so difficult?
• #### Staff Review

• Currently 4.0/5 Stars.
This lecture, the final one of the course, is about cryptography. This lesson talks about the history of cryptography, how it connects to number theory, and what it looks like today. Encoding an decoding a message is quite an interesting process, and it turns out that it is so difficult to decode messages because it is difficult to find the two prime numbers that a very large number factors into. This is a great finale to a very interesting and well-taught course.
• #### silentbang

• Currently 5.0/5 Stars.
wow.I am impressed by the way mr.ArsDigita explains the theory. that helps me a lot . thank you so much !