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