KhanAcademy Journey into cryptography

[Usr6]

Ancient cryptography Explore how we have hidden secret messages through history.

• What is cryptography?
  
• The Caesar cipher
  
• Caesar Cipher Exploration
  
• Frequency Fingerprint Exploration
  
• Polyalphabetic cipher
  
• Polyalphabetic Exploration
  
• The one-time pad
  
• Perfect Secrecy Exploration
  
• Frequency stability
  
• Frequency stability exploration
  
• Coin flip sequences
  
• The Enigma encryption machine
  
• Perfect secrecy
  
• Pseudorandom number generators
  
• Random Walk Exploration
  

Modern cryptography A new problem emerges in the 20th century. What happens if Alice and Bob can never meet to share a key in the first place?

• 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?
  

Ciphers Learn about algorithms for performing encryption & decryption. Then practice making and breaking codes!

• Ciphers vs. codes
  
• Shift cipher
  
• Caesar cipher encryption
  
• Caesar cipher decryption
  
• Caesar cipher frequency analysis
  
• Vigenere cipher encryption
  
• XOR bitwise operation
  
• XOR and the one-time pad
  
• XOR exploration
  
• Bitwise operators
  
• What's next?
  

Modular arithmetic This is a system of arithmetic for integers. These lessons provide a foundation for the mathematics presented in the Modern Cryptography tutorial.

• What is modular arithmetic?
  
• Modulo operator
  
• Congruence modulo
  
• Congruence relation
  
• Equivalence relations
  
• The quotient remainder theorem
  
• Modular addition and subtraction
  
• Modular addition
  
• Modular multiplication
  
• Modular multiplication
  
• Modular exponentiation
  
• Fast modular exponentiation
  
• Fast Modular Exponentiation
  
• Modular inverses
  
• The Euclidean Algorithm
  

Primality test Why do Primes make some problems fundamentally hard? Build machines to perform primality tests!

• Introduction
  
• Primality test challenge
  
• Trial division
  
• Running time
  
• Level 2: measuring running time
  
• Computer memory (space)
  
• Binary memory exploration
  
• Algorithmic efficiency
  
• Level 3: Challenge
  
• Sieve of Eratosthenes
  
• Level 4: Sieve of Eratosthenes
  
• Primality test with sieve
  
• Level 5: Trial division using sieve
  
• The prime number theorem
  
• Prime density spiral
  
• Prime Gaps
  
• Time space tradeoff
  
• Summary (what's next?)
  

Randomized algorithms Would access to coin flips speed up a primality test? How would this work?

• Randomized algorithms (intro)
  
• Conditional probability warmup
  
• Guess the coin
  
• Random primality test (warm up)
  
• Level 9: Trial Divison vs Random Division
  
• Fermat's little theorem
  
• Fermat primality test
  
• Level 10: Fermat Primality Test
  

Link: https://www.khanacademy.org/computing/computer-science/cryptography