Public Key Cryptography Outline

gistfile1.txt

Public Key Cryptography

The Problem: How do we communicate securely on the internet?
  - We have to encrypt our communications.
  - How do two parties who have never met, agree on a key when all of their communications are public?
  - The answer: Diffie Hellman Key Exchange. -Whitfield Diffie, Martin Hellman 
  - The first implementation of public key cryptography as envisioned by Ralph Merkle.
  
The Setup:
  - Alice wants to Talk to Bob.
  - Eve is listening into everything that Alice and Bob say.
  - You have to agree on a numerical key that Eve can't figure out even though she hears everything.
  - How is this possible?
  
Diffie-Hellman key exchange
  - Based on the idea of a one way function
  - A math equation that is easy to do in one direction but difficult in the other.
  - Math is hard, so let's do colors.
  - It's easy to mix two colors to get a third color.
  - It's hard to take one color and figure out which two colors made it.

How?
  - Agree on a starting color.
  - Randomly select a color, and mix it into public yellow.
  - Alice sends her mix to Bob.
  - Bob sends his mix to Alice.
  - They then add their secret color to the other persons mixture.
  - They both end up at the same color and this is their key.
  - Eve doesn't know what this key is because she needs one of the private colors to figure it out.
  
Math
  - Same mathematical result can be computed from different inputs.
  - 2 * 3 * 5 = 30
  - 3 * 5 * 2 = 30
  - They use modular arithmetic. It gets complicated here.
  https://www.youtube.com/watch?v=Afyqwc96M1Y if you are REALLY interested.
  
  THE END