Briefly explain Diffie Hellman key exchange.
Subject Computer and Network Security
NU Year Set: 4.(d) Marks: 6 Year: 2015

The Diffie-Hellmann key exchange is a secure method for exchanging cryptographic keys.

This method allows two parties which have no prior knowledge of each other to establish a shared, secret key, even over an insecure channel. 

The concept uses multiplicative group of integers modulo, which without knowledge of the private keys of any of the parties, would present a mathematically overwhelming task to a code breaker.

Once Alice and Bob have agreed on p and q in private, they choose positive whole-number personal keys a and b, both less than the prime-number modulus p. Neither user divulges their personal key to anyone; ideally, they memorize these numbers and do not write them down or store them anywhere. Next, Alice and Bob compute public keys a* and b* based on their personal keys according to the formulas

a* = qa mod p

and

b* = qb mod p

The two users can share their public keys a* and b* over a communications medium assumed to be insecure, such as the Internet or a corporate wide area network (WAN). From these public keys, a number x can be generated by either user on the basis of their own personal keys. Alice computes x using the formula

x = (b*)a mod p

Bob computes x using the formula

x = (a*)b mod p

The value of x turns out to be the same according to either of the above two formulas. However, the personal keys a and b, which are critical in the calculation of x, have not been transmitted over a public medium. Because it is a large and apparently random number, a potential hacker has almost no chance of correctly guessing x, even with the help of a powerful computer to conduct millions of trials. The two users can therefore, in theory, communicate privately over a public medium with an encryption method of their choice using the decryption key x.

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