The Snack-Time Diffie-Hellman Protocol
The Problem: Alice and Bob are in a meeting. They both want to figure out if the other has Potato Chips, so they can secretly coordinate a mutual snack break WITHOUT their manager, Eve, finding out and inviting herself.
The Cryptographic Solution (Snack Version):
1. Public Parameters (The Snack Rules):
· Everyone agrees on a large, prime number of hunger, p = 11.
· Everyone agrees on a base snack, g = 2 (the humble Pretzel Stick).
2. Secret Ingredients:
· Alice secretly chooses her private condiment, a = 4 (Sriracha).
· Bob secretly chooses his private condiment, b = 7 (Secret "Everything" Bagel Seasoning).
3. Public Exchange (The Office Kitchen Chat):
· Alice mixes the base snack (Pretzel) with her secret condiment (Sriracha) and leaves the result on the counter:
A = g^a mod p → 2^4 mod 11 = 16 mod 11 = 5.
She announces: "I'm feeling a '5' level of hungry."
· Bob does the same with his seasoning:
B = g^b mod p → 2^7 mod 11 = 128 mod 11 = 7.
He announces: "Yeah, I'm at a '7' myself."
4. Deriving The Shared Secret (The Snack Pact):
· Alice takes Bob's public number (7) and mixes it with her private Sriracha (4):
S = B^a mod p → 7^4 mod 11 = 2401 mod 11 = 9.
· Bob takes Alice's public number (5) and mixes it with his private Seasoning (7):
S = A^b mod p → 5^7 mod 11 = 78125 mod 11 = 9.
Eureka! They both independently arrive at the same shared secret hunger level: 9.
The Result: Alice and Bob now share a Secret Snack Index of 9. They exchange a knowing glance. At 3 PM, they simultaneously get up, walk to the vending machine, and both buy the same obscure "Spicy Nacho #9" chip bag, fulfilling their encrypted pact.
Eve (The Manager), who was listening the whole time, only heard 5 and 7. Without the Secret Condiments (a & b), she cannot compute the 9. She just thinks they're weirdly in sync about hydration. She misses the snack run.
