Diffie-Hellman: The Basics

The Diffie-Hellman Key Exchange is a method of securely exchanging cryptographic keys across insecure and untrusted networks. To do this a shared secret between two entities must be created, it does this with a mathematical one way function. A one way function is a problem that is difficult to solve in one direction, but easy in the other. Most major websites use one way function to store password hash digests rather than the users actual password.

A simple to under stand one way function can be explained with mixing paint. If you have three different colours of paint, and mix them together, it would be almost impossible to reverse engineer the mixed paint to discover the original colours.

Below is a simple to understand break down of the mechanism that Diffe-Hellman employs. It is explained both with mathematics and colours for simplicity. Bob and Alice want to create a shared secret and mutually authenticate each other, Eve wants to know what the secret is…how do Alice and Bob Stop her?

Step 1: Alice and Bob agree on of a Prime Modulus ie. 17 and a primitive root ie. 3. This is a number that when raised to any exponent (X) with modulus produces a equiprobable result. 3 is a prime root of 17.


Step 2: Alice and Bob both select random Private Keys. This number will be used as the exponent and is used as the exponent X in the agreed modulus equation. Without the Private Key this is very difficult to reverse. (A large prime modulus must be used, 17 is just for demonstration purposes)


Step 3: The results of this produce Alice and Bob’s Public Keys 6 | PURPLE and 12 | ORANGE These are then shared


Step 4: The Public keys is then shared, allowing Eve to intercept them. The private keys are kept secret so Eve does not know the private key/exponent to allow her reverse the maths to find them.
Now Alice and Bob can use each others Public Keys for the start of their Modulus equation. With their Private Key as the exponent once again.


10 | BLACK is the shared secret. Both sides will always find the same result as their Private Key is obfuscated in the Public Key. So the equations are basically the same. But Alice and Bob can workout each others Private Key. Eve can not work out the Private Keys or the Shared Secret.

This is a very basic explanation of the broad concept. Understanding each step involved here is vital, before endeavouring to learn Diffie-Hell in detail.

If you are struggling to understand this, have a look at Khan Academy’s excellent video on this subject that is presented by Birt Cruise.

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