# CRYPTOGRAPHY AND THE DIFFIE–HELLMAN Presentation by CDT Ashcraft

### 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