Diffie-Hellman Key Exchange Overview

Study Notes

Diffie-Hellman Key Exchange Algorithm Overview

Diffie-Hellman key exchange (DHKE) is a cryptographic protocol enabling two parties to securely agree on a secret key over an insecure channel.
This key facilitates secure symmetric encryption (e.g., AES) for confidentiality and integrity.
The protocol doesn't directly transmit the secret key; instead, it allows exchanging information to calculate it.

Key Idea

The core concept is enabling two parties to compute a shared secret without direct transmission, crucial for insecure communication channels like public networks.

Necessary Components

Publicly known prime number (p): A large prime number shared by both parties.
Publicly known integer (g): A primitive root modulo p. Powers of g, modulo p, produce all possible values.

Calculation Process

Party A:
- Chooses a secret integer (a).
- Calculates A = g^a mod p; this is A's public key.
- Sends A to Party B.
Party B:
- Chooses a secret integer (b).
- Calculates B = g^b mod p; this is B's public key.
- Sends B to Party A.
Party A:
- Calculates k = B^a mod p.
Party B:
- Calculates k = A^b mod p.
- Both parties now possess the identical shared secret key (k).

Secure Communication

Both parties apply the calculated shared secret key (k) for symmetric encryption (e.g., AES) to encrypt and decrypt messages.

Security Considerations (Vulnerabilities)

Man-in-the-middle attacks: An attacker intercepts the exchange, calculates their own key, and relays data, deceiving participants into using their key.
Parameter selection: Weak parameters (small primes or poorly chosen g) can be exploited by attackers. Large prime numbers (hundreds or thousands of bits) are essential.
- Attackers might identify mathematical relationships to derive secret exponents from public keys.
Implementation errors: Improper implementation can expose the secret key.

Improvements and Alternatives

Elliptic Curve Diffie-Hellman (ECDH): An alternative using elliptic curve cryptography; it often provides comparable security with smaller key sizes, beneficial for resource-constrained systems.

Summary

Diffie-Hellman is fundamental for secure communication over insecure channels.
The protocol facilitates shared key calculation without transmission.
Security heavily relies on the chosen parameters (prime number and primitive root) and proper implementation.
ECDH offers improved security and reduced computation.

Description

This quiz covers the fundamentals of the Diffie-Hellman key exchange algorithm, a critical cryptographic protocol that enables two parties to securely agree on a shared secret key over an insecure channel. It delves into the necessary components, calculation process, and its application in symmetric encryption algorithms like AES.