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Journey into Cryptography
How have humans protected their secret messages through history? Apply probability to solve an age old problem.
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Practice this topic
Ancient Cryptography
Explore how we have hidden secret messages through history.
- What is Cryptography?
- Probability Space
- Probability space
- The Caesar Cipher
- Caesar Cipher Exploration
- Frequency Fingerprint Exploration
- Polyalphabetic Cipher
- Polyalphabetic Exploration
- The One-Time Pad
- Perfect Secrecy Exploration
- Frequency Stability
- Coin flip sequences
- Frequency Stability Exploration
- The Enigma Encryption Machine (case study)
- Perfect Secrecy
- Pseudorandom Number Generators
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
- The fundamental theorem of arithmetic
- Prime density spiral
- Public Key Cryptography: what is it?
- The Discrete Logarithm Problem
- Review Modular Arithmetic
- 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?
Modular Arithmetic
This is a system of arithmetic for integers. These lessons provide
a foundation for the mathematics presented in the Modern Cryptography
tutorial.
Cryptography Challenge
Cryptography Challenge. Put your knowledge to the test!
Computational Number Theory
Why do Primes make some problems fundamentally hard? Build machines to perform primality tests!
- Primality Test
- Level 1: Primality Test
- 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 Gaps
- Time Space Tradeoff
- Summary (what's next?)
Randomized Algorithms
Checking if a number is prime turned out to be a difficult to
answer quickly. Would access to coin flips speed up a primality test?
How would this work?
- Randomized Algorithms (intro)
- Conditional Probability (Bayes Theorem) Visualized
- Guess the coin
- Random Primality Test (warm up)
- Level 9: Trial Divison vs Random Division
- Fermat's Little Theorem
- What's Next?
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Journey into Information Theory
We've always been communicating.... as we
moved from signal fires, to alphabets & electricity the problems
remained the same.
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Information Theory
Explore the history of communication from signal fires to the Information Age
- What is Information Theory?
- Prehistory: Proto-writing
- Ptolemaic: Rosetta Stone
- Ancient History: The Alphabet
- Source Encoding
- Visual Telegraphs (case study)
- Decision Tree Exploration
- Electrostatic Telegraphs (case study)
- The Battery & Electromagnetism
- Morse Code & The Information Age
- Morse code Exploration
- Symbol Rate
- Symbol Rate Exploration
- Introduction to Channel Capacity
- Message Space Exploration
- What's Next?
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