Understanding Diffie-Hellman Algorithm for Enhanced Network Security
Delve into the intricacies of the Diffie-Hellman algorithm, the first public-key cryptography method devised by Whitfield Diffie and Martin Hellman. Learn how this key exchange technique facilitates secure key exchange between users for encryption, alongside its dependence on discrete logarithm complexity.
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Presentation Transcript
Diffie-Hellman Algorithm Network Security 1
Diffie-Hellman Algorithm Objectives of the Topic After completing this topic, a student will be able to describe the Diffie- Hellman algorithm. 2
Diffie-Hellman Algorithm Figures and material in this topic have been adapted from Network Security Essentials : Applications and Standards , 2014, by William Stallings. 3
Diffie-Hellman Algorithm The first published public-key algorithm that defined public- key cryptography was published by Diffie and Hellman. It is generally referred to as the Diffie Hellman key exchange. 4
Diffie-Hellman Algorithm A number of commercial products employ this key exchange technique. 5
Diffie-Hellman Algorithm Purpose of the algorithm is to enable two users to exchange a secret key securely that then can be used for subsequent encryption of messages The algorithm itself is limited to the exchange of the keys. 6
Diffie-Hellman Algorithm Depends for its effectiveness on the difficulty of computing discrete logarithms. 7
Diffie-Hellman Algorithm The Algorithm Lets assume that there are two publicly known numbers: a prime number q and an integer that is a primitive root of q. 8
Diffie-Hellman Algorithm For a prime number p, if is a primitive root of p, then , 2, , p-1 are distinct (mod p). E.g. for prime number 19, its primitive roots are 2, 3, 10, 13, 14, and 15. Suppose the users A and B wish to create a shared key. 9
Diffie-Hellman Algorithm User A selects a random integer XA < q and computes YA = XA mod q. Similarly, user B independently selects a random integer XB < q and computes YB = XB mod q. 10
Diffie-Hellman Algorithm Each side keeps the X value private and makes the Y value available publicly to the other side. Thus, XAis A s private key and YAis A s corresponding public key, The same applies for B. 11
Diffie-Hellman Algorithm User A computes the key as K = (YB)XA mod q and User B computes the key as K = (YA)XB mod q. The result is that the two sides have exchanged a secret value. 12
Diffie-Hellman Algorithm Example: Lets take q = 353 and a primitive root of 353, = 3. A and B select private keys XA = 97 and XB = 233, respectively. 14
Diffie-Hellman Algorithm Each computes its public key: A computes YA= 397 mod 353 = 40. B computes YB= 3233 mod 353 = 248. After they exchange public keys, each can compute the common secret key: 15
Diffie-Hellman Algorithm A computes K = (YB)XA mod 353 = 24897mod 353 = 160. B computes K = (YA)XB mod 353 = 40233mod 353 = 160. an attacker would have available the following information: q = 353; = 3; YA= 40; YB= 248. 16
Diffie-Hellman Algorithm In this simple example, it would be possible by brute force to determine the secret key 160. 17
Diffie-Hellman Algorithm Security of the Diffie- Hellman algorithm: While it is relatively easy to calculate exponentials modulo a prime, it is very difficult to calculate discrete logarithms. For large primes, the latter task is considered infeasible. End 18
