Lecture Notes: Diffie-Hellman Key Exchange Algorithm What is Diffie-Hellman Key Exchange? Diffie-Hellman key exchange is a cryptographic protocol used to establish a shared secret key between two parties over an insecure channel. This shared key can then be used for encryption and decryption of subsequent communications. How Diffie-Hellman Works 1. Public Parameters: Two public parameters, a large prime number (p) and a generator (g) of the multiplicative group modulo p, are agreed upon by both parties. 2. Key Generation: Each party generates a random private key (a or b) and calculates their public key using the formula: ○ Public key = g^a mod p (for party A) ○ Public key = g^b mod p (for party B) 3. Key Exchange: The parties exchange their public keys over an insecure channel. 4. Shared Secret Calculation: Each party calculates the shared secret key using the formula: ○ Shared secret = (g^b)^a mod p = (g^a)^b mod p Advantages of Diffie-Hellman ● Secure Key Exchange: Diffie-Hellman allows two parties to establish a shared secret key over an insecure channel without revealing the key itself. ● Efficiency: Diffie-Hellman is computationally efficient and can be used in various cryptographic protocols. ● Widely Used: Diffie-Hellman is a widely used key exchange protocol and is considered a standard in cryptography. Disadvantages of Diffie-Hellman ● Man-in-the-Middle Attacks: Diffie-Hellman is vulnerable to man-in-the-middle attacks, where an attacker intercepts the public keys and replaces them with their own. ● Computational Complexity: For very large prime numbers, the calculations involved in Diffie-Hellman can be computationally intensive. Applications of Diffie-Hellman ● Secure Sockets Layer (SSL): Diffie-Hellman is used to establish a secure connection between a web server and a client, protecting data transmitted over the internet. ● Virtual Private Networks (VPNs): Diffie-Hellman is used to establish secure tunnels for VPN connections. ● Secure Shell (SSH): Diffie-Hellman is used to authenticate and encrypt data transmitted over SSH. Conclusion Diffie-Hellman key exchange is a fundamental cryptographic protocol that provides a secure way for two parties to establish a shared secret key. It is widely used in various applications and is considered a cornerstone of modern cryptography.