Diffie Hellman Key Exchange

What is Diffie Hellman Key Exchange?

Diffie-Hellman Key Exchange is a technique of securely transferring cryptographic keys over a public channel, devised by Ralph Merkle and named after Whitfield Diffie and Martin Hellman, and was one of the earliest public-key protocols. Diffie-Hellman Key Exchange is one of the earliest practical examples of public key exchange. This is the oldest publicly known paper that proposed the idea of a private key and a corresponding public key. It was published in 1976 by Diffie and Hellman.

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This algorithm's security is primarily based on the difficulty of computing discrete logarithms. Many protocols use the Diffie-Hellman algorithm to improve security, and a few examples are: Secure Shell (SSH), Transport Layer Security (TLS), Secure Sockets Layer  (SSL),Public Key Infrastructure (PKI), etc.

Key points to be noted:

  • Its not an encryption algorithm.
  • Its used to exchange secret keys between users(sender and receiver over a network).
  • It uses asymmetric encryption to exchange the secret key.

Why we use this algorithm?

Its because while sharing key between two users it can be stolen, so for the security purposes we use this algorithm. Now we'll look at how this algorithm works:-

First thing we have got is a prime number ‘n’. And then there is ‘generator’ - ‘g’. It must be selected in such way that it is a primitive rootof‘n’, alsog<n.

NOTE: ‘a’ is a primitive root of ‘n’ if – a mod n , a2 mod n, a3mod n, ……, an-1 mod n - gives result : {1,2,3,….,n-1} i.e., values should not be repeated and we should have all values in the output set from 1 to n-1.

Now, Lets assume two users – Alice and Bob and corresponding to them they have their private keys as – (a – red coloured) and (b – blue coloured)respectively.The generator(g – lightgreencoloured) and the prime number(n) always remain in the public key area.

First the public key of both the users will be joined with the generator (g).

We got (ag – orange coloured) public key of Alice and (bg – green coloured) public key of Bob.

Now, these keys will be exchanged by both users as –Alice will take the Bob’s public key (bg) and Bob will take Alice’s public key (ag).

And combine it with their private key and both will get a SHAREDSECRET KEY (abg) which is common for both users that we needed.

Now you can see we got our required condition of a shared keyused in asymmetric encryption.

Also it cannot be cracked in the public area as we got public keys – (ag) and (bg), so to derive the shared secret key from them the attacker would need to separate the (ag) and (bg) public key which is the an extremely difficult task to perform.

Also the pros of this algorithm is that : Both persons don’t need any info from each other. They just use ‘g’ and ‘n’ which are known to all publicly.

NOTE: generator(g) and prime number (n) is global public element (known to everyone)

So, this was process Diffie-Hellman Key Exchange use.

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