🔢Learn Modular Arithmetic Basics: Clock Math That Secures the Internet
Start with the clock on your wall and finish by encrypting a short message with a toy RSA example, using primes you pick yourself. You'll feel modular arithmetic as a living tool, not a programming operator.
Phase 1Clocks, Wraparound, and Equivalence Classes
Feel wraparound and equivalence classes through clocks
Your clock is already doing modular arithmetic
5 minYour clock is already doing modular arithmetic
Two numbers are 'the same' if they differ by a multiple of n
6 minTwo numbers are 'the same' if they differ by a multiple of n
Mod n turns infinity into a ring of n numbers
6 minMod n turns infinity into a ring of n numbers
You can reduce at every step without breaking anything
6 minYou can reduce at every step without breaking anything
Phase 2Arithmetic Inside a Finite World
Compute sums, products, and inverses mod small primes
Subtraction mod n is addition in disguise
5 minSubtraction mod n is addition in disguise
Build a multiplication table and spot the zeros
7 minBuild a multiplication table and spot the zeros
Some numbers have a multiplicative inverse — and some don't
7 minSome numbers have a multiplicative inverse — and some don't
Fast exponentiation: square, reduce, repeat
8 minFast exponentiation: square, reduce, repeat
Mod a prime, a^(p−1) always equals 1
7 minMod a prime, a^(p−1) always equals 1
Phase 3Where Modular Math Already Runs
See modular math inside RSA, hashing, and ISBNs
Your dictionary lookup relied on mod the whole time
6 minYour dictionary lookup relied on mod the whole time
The barcode on your book was mod 11
7 minThe barcode on your book was mod 11
What day of the week will Nov 7, 2055 be?
7 minWhat day of the week will Nov 7, 2055 be?
RSA is just Fermat's theorem wearing a suit
8 minRSA is just Fermat's theorem wearing a suit
Phase 4Your Own Toy RSA Cipher
Encrypt a short message using a toy RSA
Encrypt a short message with your own toy RSA
8 minEncrypt a short message with your own toy RSA
Frequently asked questions
- What is modular arithmetic in simple terms?
- This is covered in the “Learn Modular Arithmetic Basics: Clock Math That Secures the Internet” learning path. Start with daily 5-minute micro-lessons that build from fundamentals to hands-on application.
- Why is modular arithmetic used in cryptography like RSA?
- This is covered in the “Learn Modular Arithmetic Basics: Clock Math That Secures the Internet” learning path. Start with daily 5-minute micro-lessons that build from fundamentals to hands-on application.
- How is the mod operator different from 'true' modular arithmetic?
- This is covered in the “Learn Modular Arithmetic Basics: Clock Math That Secures the Internet” learning path. Start with daily 5-minute micro-lessons that build from fundamentals to hands-on application.
- What is Fermat's little theorem and why does it matter?
- This is covered in the “Learn Modular Arithmetic Basics: Clock Math That Secures the Internet” learning path. Start with daily 5-minute micro-lessons that build from fundamentals to hands-on application.
- Can I really do RSA by hand with small primes?
- This is covered in the “Learn Modular Arithmetic Basics: Clock Math That Secures the Internet” learning path. Start with daily 5-minute micro-lessons that build from fundamentals to hands-on application.
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