Follow these steps to understand and simulate the Diffie-Hellman key exchange protocol:

Step 1: Public Information Setup

• Click the "Generate Prime" button to select a large prime number (p)
• The system will automatically set a corresponding generator (g) for the selected prime
• Click "Another Generator" to cycle through different valid generators for the current prime
• Note: Both the prime number and generator are public information that can be shared openly

Step 2: Private Key Generation

• Alice's Side:
  • Click "Generate A" to create Alice's private key (a)
  • This private key must be kept secret by Alice
• Bob's Side:
  • Click "Generate B" to create Bob's private key (b)
  • This private key must be kept secret by Bob

Step 3: Public Key Calculation

• Alice's Side:
  • Click "Calculate g^a" to compute Alice's public key using the formula: g^a mod p
  • This public key can be shared openly
• Bob's Side:
  • Click "Calculate g^b" to compute Bob's public key using the formula: g^b mod p
  • This public key can be shared openly

Step 4: Key Exchange

• Alice's Side:
  • Click "Send Public Key to Bob" to transfer Alice's public key (g^a mod p) to Bob
• Bob's Side:
  • Click "Send Public Key to Alice" to transfer Bob's public key (g^b mod p) to Alice

Step 5: Shared Secret Calculation

• Alice's Side:
  • Click "Calculate Shared Secret" to compute the final shared secret using Bob's public key
  • Formula: (g^b)^a mod p = g^(ab) mod p
• Bob's Side:
  • Click "Calculate Shared Secret" to compute the final shared secret using Alice's public key
  • Formula: (g^a)^b mod p = g^(ab) mod p

Step 6: Verification

• Compare the shared secret values calculated by both Alice and Bob
• Success: If both values are identical, the Diffie-Hellman key exchange has been completed successfully
• Security: Note that even though all public information was transmitted openly, the shared secret remains secure due to the computational difficulty of the discrete logarithm problem

Understanding the Security

• Public Information: Prime (p), Generator (g), Alice's public key (g^a mod p), Bob's public key (g^b mod p)
• Private Information: Alice's private key (a), Bob's private key (b)
• Shared Secret: g^(ab) mod p - known only to Alice and Bob
• Eavesdropper's Challenge: Cannot compute g^(ab) mod p from the public information without solving the discrete logarithm problem