# Instructions

Diffie-Hellman key exchange.

Alice and Bob use Diffie-Hellman key exchange to share secrets.
They start with prime numbers, pick private keys, generate and share public keys, and then generate a shared secret key.

## Step 0

The test program supplies prime numbers p and g.

## Step 1

Alice picks a private key, a, greater than 1 and less than p.
Bob does the same to pick a private key b.

## Step 2

Alice calculates a public key A.

    A = gᵃ mod p

Using the same p and g, Bob similarly calculates a public key B from his private key b.

## Step 3

Alice and Bob exchange public keys.
Alice calculates secret key s.

    s = Bᵃ mod p

Bob calculates

    s = Aᵇ mod p

The calculations produce the same result!
Alice and Bob now share secret s.
