Diffie-Hellman algorithm:

The Diffie-Hellman algorithm is being used to establish a shared secret that can be used for secret communications while exchanging data over a public network using the elliptic curve to generate points and get the secret key using the parameters.

For the sake of simplicity and practical implementation of the algorithm, we will consider only 4 variables, one prime P and G (a primitive root of P) and two private values a and b.
P and G are both publicly available numbers. Users (say Alice and Bob) pick private values a and b and they generate a key and exchange it publicly. The opposite person receives the key and that generates a secret key, after which they have the same secret key to encrypt.

Alice	Bob
Public Keys available = P, G	Public Keys available = P, G
Private Key Selected = a	Private Key Selected = b
Key generated = x = G^a mod P	Key generated = y = G^b mod P
Exchange of generated keys takes place
Key received = y	Key received = x
Generated Secret Key = k_a = y^a mod P	Generated Secret Key = k_b = x^b mod P
Algebraically, it can be shown that k_a = k_b
Users now have a symmetric secret key to encrypt

Example:

Step 1: Alice and Bob get public numbers P = 23, G = 9
Step 2: Alice selected a private key a = 4 and
Bob selected a private key b = 3
Step 3: Alice and Bob compute public values
Alice: $x =(9^4 mod 23)$ = (6561 mod 23) = 6
Bob: $y = (9^3 mod 23)$ = (729 mod 23) = 16
Step 4: Alice and Bob exchange public numbers
Step 5: Alice receives public key y =16 and
Bob receives public key x = 6
Step 6: Alice and Bob compute symmetric keys
Alice: $ka = y^a mod p$ = 65536 mod 23 = 9
Bob: $kb = x^b mod p$ = 216 mod 23 = 9
Step 7: 9 is the shared secret.

Implementation:

/* This program calculates the Key for two persons
using the Diffie-Hellman Key exchange algorithm using C++ */
#include <cmath>
#include <iostream>

using namespace std;

// Power function to return value of a ^ b mod P
long long int power(long long int a, long long int b,
                    long long int P)
{
    if (b == 1)
        return a;

    else
        return (((long long int)pow(a, b)) % P);
}

// Driver program
int main()
{
    long long int P, G, x, a, y, b, ka, kb;

    // Both the persons will be agreed upon the
    // public keys G and P
    P = 23; // A prime number P is taken
    cout << "The value of P : " << P << endl;

    G = 9; // A primitive root for P, G is taken
    cout << "The value of G : " << G << endl;

    // Alice will choose the private key a
    a = 4; // a is the chosen private key
    cout << "The private key a for Alice : " << a << endl;

    x = power(G, a, P); // gets the generated key

    // Bob will choose the private key b
    b = 3; // b is the chosen private key
    cout << "The private key b for Bob : " << b << endl;

    y = power(G, b, P); // gets the generated key

    // Generating the secret key after the exchange
    // of keys
    ka = power(y, a, P); // Secret key for Alice
    kb = power(x, b, P); // Secret key for Bob
    cout << "Secret key for the Alice is : " << ka << endl;

    cout << "Secret key for the Bob is : " << kb << endl;

    return 0;
}
// This code is contributed by Pranay Arora

Output

The value of P : 23 The value of G : 9 The private key a for Alice : 4 The private key b for Bob : 3 Secret key for the Alice is : 9 Secret key for the Bob is : 9