Diffie-Hellman Key Exchange

First published at:


Diffie-Hellman Key Exchange is a popular mathematical key exchange algorithm. It allows two parties to establish a ‘key’ over an insecure medium such as the internet. As you will see, it doesn’t matter whether the intercepting party captures each piece of transmitted information, they will not be able to break the key in any way, other than the usual brute force method.

Diffie-Hellman Key Exchange is not an encryption method, it is generall but not always used pre encryption to decide on a shared encryption key.

We will call the communicating parties Bill and Ben. Let Roger be the intercepting party. You can work out these calculations on a calculator:

Bill and Ben transmit and agree on a public prime number (p) and a ‘generator’ (g) which is an integer less than ‘p’. Bill now decides on a random private number (a) which he does not transmit, Ben also agrees on a random private number (b) which he does not transmit either.

In this example, Bill and Ben decide that:

Roger catches p(137) and g(13)

Bill decides privately that a=31
Ben decides privately that b=23

In actual fact these numbers will be much larger to hinder brute force. We’re going to use small numbers in our example though.

Bill now computes:
j = (ga)modp [ programatically j=(g^a)%p]
j = (1331)mod137
j = 20

Ben now computes:
k = (gb)modp [ programatically k=(g^b)%p ]
k = (1323)mod137
k = 24

Ben now transmits k to Bill, and Bill transmits j to Ben
Roger captures (j)20 and (k)24

Bill now computes:

x = kamodp [programatically =(k^a)%p
x = 2431mod137
x = 91

Bill now knows that the shared encryption key is 72. He does not [need to] transmit it.

Ben calculates:

x = jbmodp [programatically =(j^b)%p
x = 2023mod137
x = 92

Ben also now knows that the shared encryption key is 72. He does not [need to] transmit it.

At this point, expand outwards:

x = 92
x = jbmodp = kamodp
((ga)modp)bmodp == ((gb)modp)amodp

Despite the fact that Roger has caught each individual transmission, j, k, g, and p, he can not work out x.

Now that both sides know the key, we can now agree that they’re going to encrypt using AAE - Adam’s Amazing Encryption.

Bob takes his phrase to encrypt - “password” and adds ‘72′ to each character using the ASCII alphabet:

Bob can now turn his phrase to a hex string:


And then add 72 to each character, making sure it wraps around 255:


Ben can now decrypt using the opposite method.

In actual fact, not only would the key be substantially longer than ‘72′, but our encryption algorithm of choice ‘AAE’ would also be replaced with something more cryptographically sound :-) - Possibly RC4



White Paper
Linux Management with Red Hat Satellite: Measuring Business Impact and ROI

Linux has become a key foundation for supporting today's rapidly growing IT environments. Linux is being used to deploy business applications and databases, trading on its reputation as a low-cost operating environment. For many IT organizations, Linux is a mainstay for deploying Web servers and has evolved from handling basic file, print, and utility workloads to running mission-critical applications and databases, physically, virtually, and in the cloud. As Linux grows in importance in terms of value to the business, managing Linux environments to high standards of service quality — availability, security, and performance — becomes an essential requirement for business success.

Learn More

Sponsored by Red Hat

White Paper
Private PaaS for the Agile Enterprise

If you already use virtualized infrastructure, you are well on your way to leveraging the power of the cloud. Virtualization offers the promise of limitless resources, but how do you manage that scalability when your DevOps team doesn’t scale? In today’s hypercompetitive markets, fast results can make a difference between leading the pack vs. obsolescence. Organizations need more benefits from cloud computing than just raw resources. They need agility, flexibility, convenience, ROI, and control.

Stackato private Platform-as-a-Service technology from ActiveState extends your private cloud infrastructure by creating a private PaaS to provide on-demand availability, flexibility, control, and ultimately, faster time-to-market for your enterprise.

Learn More

Sponsored by ActiveState