Diffie-Hellman Key Exchange

Goal: To exchange cryptographic keys over a public channel.
Then we can encrypt all future communication!

Prereqs:

A prime number greater than 2, p.

A primitive root modulo of p which we'll call g.

A secret integer for each party generating the secret key: a and b.

value muse be less than p but greater than 1.

Operations:

Person with a calculates A and sends the result publicly to b while b does the same for B.

Each person can use the capital letter variables and some fancy exponent and modulo math to calculate a shared secret key (s below) which will be super difficult for a third party to figure out given only the publicly available variables p, g, A, B.

Establish givens which will be public

Allie

Choose a secret integer for Allie

Calculations:

A = g^a modulo p =

Then we send A over to the other person. This will be assumed to be publicly accessible. Wait for B to be sent from the other person to calculate the secret.

B = ?

Once we have B we can calculate the secret.

S = B^a modulo p = ?

Butch

Choose a secret integer for Butch

Calculations:

B = g^b modulo p =

Then we send B over to the other person. This will be assumed to be publicly accessible. Wait for A to be sent from the other person to calculate the secret.

A = ?

Once we have A we can calculate the secret.

S = A^b modulo p = ?