The Problem
Alice and Bob want to communicate privately. They need a shared secret key to encrypt their messages.
But they’re on the internet. Eve is watching everything they send.
How do they agree on a secret key without Eve learning it?
Before 1976
The only options were:
- Meet in person and exchange the key
- Use a trusted courier to deliver the key
- Pre-share keys before you need them
None of these work well for the internet. You can’t meet everyone you want to talk to.
The Breakthrough
In 1976, Whitfield Diffie and Martin Hellman published a paper that changed everything.
They showed that two people can create a shared secret by exchanging messages in public. Even if an attacker sees every message, they can’t figure out the secret.
Key exchange: Creating a shared secret over an insecure channel.
This was the birth of public-key cryptography.
The Intuition
Think of it like mixing paint.
Step 1: Alice and Bob agree on a public color. Say, yellow. Everyone knows this.
Step 2: Each picks a secret color. Alice picks red. Bob picks blue.
Step 3: Each mixes the public color with their secret.
- Alice: yellow + red = orange
- Bob: yellow + blue = green
Step 4: They exchange their mixed colors publicly.
Eve sees orange and green. But she can’t “unmix” them to get the secrets.
Step 5: Each adds their secret to what they received.
- Alice: green + red = brown
- Bob: orange + blue = brown
They get the same final color!
Why It Works
Both end up with: public + Alice’s secret + Bob’s secret
The order of mixing doesn’t matter. Both paths lead to the same result.
Eve only sees:
- The public color (yellow)
- Alice’s mix (orange = yellow + red)
- Bob’s mix (green = yellow + blue)
She never sees the individual secrets. And she can’t unmix paint.
From Paint to Math
Real Diffie-Hellman uses math instead of paint.
The “mixing” operation is modular exponentiation: raising a number to a power, then taking the remainder.
The “can’t unmix” property comes from the Discrete Logarithm Problem: given the result, finding the exponent is extremely hard.
The next section shows the actual calculations.