Implementation of DiffieHellman Algorithm (original) (raw)

Implementation of Diffie-Hellman Algorithm

Last Updated : 3 Feb, 2026

**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.

Step-by-Step explanation is as follows:

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 = 5
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 =(5^4 mod 23) = (625 mod 23) = 4
Bob: y = (5^3 mod 23) = (125 mod 23) = 10
Step 4: Alice and Bob exchange public numbers
Step 5: Alice receives public key y =10 and
Bob receives public key x = 4
Step 6: Alice and Bob compute symmetric keys
Alice: ka = y^a mod p = 10000 mod 23 = 18
Bob: kb = x^b mod p = 64 mod 23 = 18
Step 7: 18 is the shared secret.

You can find more detail on what primitive roots of a number are in this article : Primitive root of a prime number n modulo n.

For our example the number 23(prime) has the following primitive roots : [5, 7, 10, 11, 14, 15, 17, 19, 20, 21].

C++ `

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

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 = 5; // 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

C

/* This program calculates the Key for two persons using the Diffie-Hellman Key exchange algorithm */ #include <math.h> #include <stdio.h>

// 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
printf("The value of P : %lld\n", P);

G = 5; // A primitive root for P, G is taken
printf("The value of G : %lld\n\n", G);

// Alice will choose the private key a
a = 4; // a is the chosen private key
printf("The private key a for Alice : %lld\n", a);
x = power(G, a, P); // gets the generated key

// Bob will choose the private key b
b = 3; // b is the chosen private key
printf("The private key b for Bob : %lld\n\n", b);
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

printf("Secret key for the Alice is : %lld\n", ka);
printf("Secret Key for the Bob is : %lld\n", kb);

return 0;

}

Java

// This program calculates the Key for two persons // using the Diffie-Hellman Key exchange algorithm class GFG {

// Power function to return value of a ^ b mod P
private static long power(long a, long b, long p)
{
    if (b == 1)
        return a;
    else
        return (((long)Math.pow(a, b)) % p);
}

// Driver code
public static void main(String[] args)
{
    long P, G, x, a, y, b, ka, kb;

    // Both the persons will be agreed upon the
    // public keys G and P

    // A prime number P is taken
    P = 23;
    System.out.println("The value of P:" + P);

    // A primitive root for P, G is taken
    G = 5;
    System.out.println("The value of G:" + G);

    // Alice will choose the private key a
    // a is the chosen private key
    a = 4;
    System.out.println("The private key a for Alice:"
                       + a);

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

    // Bob will choose the private key b
    // b is the chosen private key
    b = 3;
    System.out.println("The private key b for Bob:"
                       + b);

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

    // 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

    System.out.println("Secret key for the Alice is:"
                       + ka);
    System.out.println("Secret key for the Bob is:"
                       + kb);
}

}

// This code is contributed by raghav14

Python

Diffie-Hellman Code

Power function to return value of a^b mod P

def power(a, b, p): if b == 1: return a else: return pow(a, b) % p

Main function

def main(): # Both persons agree upon the public keys G and P # A prime number P is taken P = 23 print("The value of P:", P)

# A primitive root for P, G is taken
G = 5
print("The value of G:", G)

# Alice chooses the private key a
# a is the chosen private key
a = 4
print("The private key a for Alice:", a)

# Gets the generated key
x = power(G, a, P)

# Bob chooses the private key b
# b is the chosen private key
b = 3
print("The private key b for Bob:", b)

# Gets the generated key
y = power(G, b, P)

# 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

print("Secret key for Alice is:", ka)
print("Secret key for Bob is:", kb)

if name == "main": main()

C#

// C# implementation to calculate the Key for two persons // using the Diffie-Hellman Key exchange algorithm using System; class GFG {

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

    else
        return (((long)Math.Pow(a, b)) % P);
}
public static void Main()
{
    long 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
    Console.WriteLine("The value of P:" + P);

    G = 5; // A primitive root for P, G is taken
    Console.WriteLine("The value of G:" + G);

    // Alice will choose the private key a
    a = 4; // a is the chosen private key
    Console.WriteLine("\nThe private key a for Alice:"
                      + a);
    x = power(G, a, P); // gets the generated key

    // Bob will choose the private key b
    b = 3; // b is the chosen private key
    Console.WriteLine("The private key b for Bob:" + b);
    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

    Console.WriteLine("\nSecret key for the Alice is:"
                      + ka);
    Console.WriteLine("Secret key for the Alice is:"
                      + kb);
}

}

// This code is contributed by Pranay Arora

JavaScript

**Output:

Screenshot-2026-02-03-171959