1. CRYPTOGRAPHY AND THE DIFFIE–HELLMAN KEY EXCHANGE Presentation by CDT Ashcraft

2. 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.

3. 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.

4. 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?

7. 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

8. ONE WAY FUNCTION

9.  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.

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