### CRYPTOGRAPHY AND THE

*DIFFIE–HELLMAN *KEY EXCHANGE

Presentation by CDT Ashcraft

### ORIGIN

Following WWII, tensions between the USSR and the United States necessitated a way to both launch and defend against nuclear attacks from Intercontinental Ballistic Missiles (ICBM)

An important defense: the semiautomatic ground environment, automated system of 100 long-distance radars that transmitted tracking data, fed into primary warning center in Colorado. Machine to machine communication allowed operators to make split-second decisions using information transmitted and processed automatically by computers.

Computer Networking, Finances, Education.

Internet grows, problem emerges.

### ENCRYPTING DATA

Required sharing a secret number, known as the “Key”

* Symmetric key crypto lets two parties share secret messages **as long as * they already have a shared key

** How can two people who have never met agree on a secret shared key without a third party, who is listening, also obtaining a copy???**

** Scenario: Alice and Bob are communicating on an unsecured network.**

### EVE THE EAVESDROPPER

Eve is an attacker who can see Alice and Bob’s messages

She cannot modify them

She is a *Passive attacker*

Examples:

Unencrypted wifi users

Government

Internet provider

Someone else on the same network

**Alice and Bob need a way to encrypt messages, but how do they choose?**

### MODULAR ARITMATIC

We need a numerical procedure that is easy in one direction and difficult in the opposite direction

mod p

Clock Arithmetic

Pick a prime modulus such as 17

Use a prime root of 17, such as 3

3^x mod 17 = [0,16] equally likely

Reverse procedure is difficult to find

Discrete Logarithm

### ONE WAY FUNCTION

To solve, it is easy with small numbers, but with big number it becomes impractical

Using a prime modulus hundreds on digits long, it could take thousands of years to solve using computers

The strength of a One Way Function is based on the time needed to reverse it.

Bob and Alice each come to a solution that is not known to Eve, an eavesdropping attacker