Explain how DiffeHellman key exchange protocol can share a s

Explain how Diffe-Hellman key exchange protocol can share a secret value without divulging it to any other person and show an example.

Solution

Answer :-

Diffe-Hellman key exchange :

Diffe-Hellman is a specific method of securely exchanging cryptographic keys over a public channel and was one of the first public-key protocols .

Diffe-Hellman it\'s implement to public key exchange implemented within the field of cryptography.

Cryptographic explanation :

The simplest and the original implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime, and g is a primitive root modulo p. These two values are chosen in this way to ensure that the resulting shared secret can take on any value from 1 to p–1. Here is an example of the protocol, with non-secret values in blue, and secret values in thick black color.

1) Alice and Bob agree to use a modulus p = 23 and base g = 5 (which is a primitive root modulo 23).
2) Alice chooses a secret integer a = 6, then sends Bob A = ga mod p
A = 56 mod 23 = 8
3) Bob chooses a secret integer b = 15, then sends Alice B = gb mod p
B = 515 mod 23 = 19
4) Alice computes s = Ba mod p
s = 196 mod 23 = 2
5) Bob computes s = Ab mod p
s = 815 mod 23 = 2
6) Alice and Bob now share a secret (the number 2).