Introduction to Cryptography
The math that keeps secrets: how your messages stay private even when everyone can see them go by.
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Big Idea
Societal Impact
Grade bands
K-2 · 3-5 · 6-8 · 9-12
AI literacy pillar
How AI works · Ethics
Lesson overview
The math that keeps secrets: how your messages stay private even when everyone can see them go by. This module climbs from an everyday intuition to the real mechanism, then names the Stanford course it descends from.
Teacher script · ~45 min
- 0–5
Hook
A code swaps each letter for another so only someone with the key can read it. Kids' versions are easy to crack. Real cryptography asks: how do we scramble messages so that even a powerful attacker who knows the method, but not the key, learns nothing? That precision is the whole subject.
- 5–15
Explore
Students do the activity in pairs: Multiply 61 x 53 in seconds. Now factor 3233 back into two primes without peeking. The gap in difficulty is what secures the internet.
- 15–30
Explain
Cryptography's real rigor is refusing to hand-wave 'secure.' It defines exactly what an attacker can do and proves the scheme leaks nothing useful even then. Security reduces to hard math problems (like factoring). The deep lesson: you don't trust a cipher because it 'looks scrambled'; you trust it because breaking it would solve a problem believed to be impossibly hard.
- 30–40
Connect to the summit
Show students this is the real thing professionals build: CS255, the real thing. The math that keeps secrets: how your messages stay private even when everyone can see them go by.
- 40–45
Check
Run the formative check below. Anyone who can explain a key term in their own words has it.
Student activity
Multiply 61 x 53 in seconds. Now factor 3233 back into two primes without peeking. The gap in difficulty is what secures the internet.
Slides
Formative check
- 1.In your own words, what is "Symmetric encryption"? (Looking for: Both sides share one secret key to lock and unlock messages.)
- 2.In your own words, what is "Public-key crypto"? (Looking for: A public key locks, a separate private key unlocks, no shared secret needed first.)
- 3.In your own words, what is "Hash function"? (Looking for: A one-way fingerprint of data: easy to compute, infeasible to reverse.)
Carry-away concepts
- Symmetric encryption
- Both sides share one secret key to lock and unlock messages.
- Public-key crypto
- A public key locks, a separate private key unlocks, no shared secret needed first.
- Hash function
- A one-way fingerprint of data: easy to compute, infeasible to reverse.
- Security reduction
- Proving a scheme is safe by showing a break would solve a known-hard problem.
From the summit · the Stanford source
You study symmetric and public-key cryptography, hash functions, and protocols, with rigorous definitions of what 'secure' even means.
This module descends from CS255 at Stanford. Students who climb the full ladder arrive here.