Walter Taylor
March 29, 2013
Computer Security
Kris Rowley
Cryptography

Diffie-Hellman Key Exchange

What it is: A specific method for exchanging cryptographic keys in which two users can communicate through a secret key and a public key (Problem). “The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in blue, and secret values in boldface red: Alice| | Bob|

Secret| Public| Calculates| Sends| Calculates| Public| Secret| a| p, g| | p,g| | | b|
a| p, g, A| ga mod p = A| A| | p, g| b|
a| p, g, A| | B| gb mod p = B| p, g, A, B| b|
a, s| p, g, A, B| Ba mod p = s| | Ab mod p = s| p, g, A, B| b, s|
| | |
1. Alice and Bob agree to use a prime number p=23 and base g=5. 2. Alice chooses a secret integer a=6, then sends Bob A = ga mod p * A = 56 mod 23
* A = 15,625 mod 23
* A = 8
3. Bob chooses a secret integer b=15, then sends Alice B = gb mod p * B = 515 mod 23
* B = 30,517,578,125 mod 23
* B = 19
4. Alice computes s = B a mod p
* s = 196 mod 23
* s = 47,045,881 mod 23
* s = 2
5. Bob computes s = A b mod p
* s = 815 mod 23
* s = 35,184,372,088,832 mod 23
* s = 2
6. Alice and Bob now share a secret: s = 2. This is because 6*15 is the same as 15*6. So somebody who had known both these private integers might also have calculated s as follows: * s = 56*15 mod 23

* s = 515*6 mod 23
* s = 590 mod 23
* s = 807,793,566,946,316,088,741,610,050,849,573,099,185,363,389,551,639,556,884,765,625 mod 23 * s = 2 (‘Cryptography’).”

Pros: It’s hard to perform a man-in-the-middle attack (Problem).

Cons: It doesn’t require any authentication (“Cryptography”).

General Information: The Diffie-Hellman key exchange is also known...

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