Discrete Log Problem & Diffie-Hellman Key Exchange Cheat Sheet

Discrete Log Problem (DLP)

• Definition: Finding x in h = g^x mod p.
• Challenge: Computationally infeasible with large prime numbers.
• Significance: Foundation of cryptographic algorithms.
• Usage: Basis for various cryptographic schemes ensuring data privacy.

Diffie-Hellman Key Exchange

• Objective: Establish a shared secret key over an insecure channel.
• Mathematical Process:
  • Initialization: Agree on p (prime number) and g (base).
  • Private Values: Each party selects a private value (a and b).
  • Public Values: Compute public values:
    • Party A computes A = g^a mod p.
    • Party B computes B = g^b mod p.
  • Key Generation:
    • Party A computes the shared key: K = B^a mod p.
    • Party B computes the shared key: K = A^b mod p.
  • Secure Communication: Both parties now possess the same shared key (K).
• Applications: TLS/SSL, VPNs, secure web browsing.
• Advantages: Simplicity, robustness, and secure key exchange without pre-sharing keys.

Conclusion

• Importance: DLP forms the bedrock of secure communication protocols.
• Essential Understanding: Crucial for safeguarding digital interactions and ensuring confidentiality.