Diffie Hellman key exchange algorithm

This article will cover the Diffie-Hellman key exchange algorithm and explain how Diffie Hellman algorithm functions, providing an example of generating a shared secret key, and offering a Java implementation of the algorithm.

  • Diffie-Hellman algorithm is a key exchange protocol used to establish a shared secret key between two communication parties over an insecure channel.
  • This algorithm facilitates the exchange of a secret key securely among users.
  • The key can be subsequently used for encryption/decryption of an information
    using a symmetric cipher.
  • The effectiveness of the Diffie Hellman key exchange algorithm depends on the difficulty of computing.
  • discrete logarithms

How Does Diffie-Hellman Work?

  1. Initialization:
    • Alice and Bob agree on two public numbers: a prime number p and a base g These values are known to both parties and are not kept secret.
    • Alice generates her private key called a; which is generated randomly and privately.
      • Bob generates his private key called b which is also a generated randomly and kept private.
  2. Calculation of Public Keys:
    • Alice computes her public key called A using the formula A = g ^ a mod p
    • Bob computes his public key B using the formula B = g ^ b mod  p
  3. Exchange of Public Keys:
    • Alice sends her public key A to Bob.
    • Bob sends his public key B to Alice.
  4. Shared Secret Calculation:
    • Alice computes the shared secret key called K using Bob’s public key B where K = B^a mod p.
    • Bob computes the shared secret key called K using Alice’s public key A where K = A ^ b mod p.
  5. Conclusion:
    • Both Alice and Bob now have the same shared secret key K, which they can use for secure communication.
    • The shared secret key K is the same for both parties, Bob and Alice but cannot be easily derived by an eavesdropper due to the difficulty of solving the discrete logarithm problem.

This above step by step algorithm shows how Alice and Bob derive a shared secret key over an insecure channel without explicitly transmitting the key itself.

Numerical Example Diffie-Hellman

Let’s illustrate with numbers: p=23, g=5, a=6, b=15.

  • Alice will compute her public key called A which is given by A= g^a mod p = 5 ^ 6 mod  23= 8, so A = 8
  • Similarly, Bob calculates his public key called B which is given by B= g^b mod p, 𝐵=5^15 mod  23=19, so B = 19
  • Alice and Bob compute the Shared Secret: by formulae
    • Alice compute shared secret key K= B ^ a mod p = 19 ^ 6 mod 23 = 2
    • Bob compute shared secret key K = A ^ b mod p = 8 ^ 15 mod 23 = 2

Attacks on Diffie-Hellman algorithm

Clogging attacks and man-in-the-middle attacks are types of vulnerabilities associated with the Diffie-Hellman algorithm, as detailed below.

Clogging Attack

  • This attack involves overwhelming the communication channel with a large number of requests.
  • By flooding the channel with requests, the attacker aims to disrupt or delay the Diffie-Hellman key exchange process.
  • The goal is to exhaust the resources of the system or network, making it difficult for legitimate parties to complete the key exchange securely.
  • Countermeasures against clogging attacks typically involve implementing rate limiting, access controls, or using secure communication protocols that can handle high traffic loads efficiently.

Man-in-the-Middle Attack

  • In this attack, the adversary intercepts and potentially alters the communication between two parties who are performing the Diffie-Hellman key exchange.
  • The attacker secretly relays and possibly modifies messages between the parties, making them believe they are directly communicating with each other.
  • By doing so, the attacker can obtain the shared secret key or manipulate the exchanged data.
  • Countermeasures for man-in-the-middle attacks include using secure channels like HTTPS, implementing cryptographic authentication, and verifying the identity of communication endpoints using digital signatures or certificates.

Diffie Hellman key exchange algorithm Advantages and Disadvantages


  • Key exchange over insecure channels. No need for pre-shared keys.
  • Scalable and efficient for secure communication.


  • Diffie Hellman key exchange algorithm is vulnerable to man-in-the-middle attacks without additional measures.
  • Relies on large prime numbers for security, which can be computationally intensive.

Comparison with Other Algorithms

  • RSA vs. Diffie-Hellman: RSA is for encryption and digital signatures, while Diffie-Hellman is for key exchange.
  • AES vs. Diffie-Hellman: AES is for symmetric encryption, and Diffie-Hellman establishes a shared secret key for encryption.

Diffie-Hellman key exchange algorithm java code

import java.math.BigInteger;

public class DiffieHellman {

    private static BigInteger calculateKey(BigInteger p, BigInteger g, BigInteger privateKey) {
        return g.modPow(privateKey, p);

    public static void main(String[] args) {
        BigInteger p = new BigInteger("23");
        BigInteger g = new BigInteger("5");
        BigInteger privateKeyA = new BigInteger("6");
        BigInteger privateKeyB = new BigInteger("15");

        BigInteger publicKeyA = calculateKey(p, g, privateKeyA);
        BigInteger publicKeyB = calculateKey(p, g, privateKeyB);

        BigInteger secretKeyA = publicKeyB.modPow(privateKeyA, p);
        BigInteger secretKeyB = publicKeyA.modPow(privateKeyB, p);

        System.out.println("Shared Secret Key for A: " + secretKeyA);
        System.out.println("Shared Secret Key for B: " + secretKeyB);

The above Java code implement the Diffie Hellman key generation process for two parties. Here is a video example of the Diffie-Hellman key exchange algorithm.

In conclusion, the Diffie-Hellman algorithm remains a fundamental tool in cryptography which enables to a secure communication in an insecure environment. Understanding its principles, advantages, and limitations is key to implementing robust encryption strategies.