Diffie-Hellman Key Exchange Simulation

Parameters

Educational Purpose: This simulation uses small numbers for demonstration. Real implementations use much larger prime numbers (typically 1024-4096 bits) for security.

Prime (p): A prime number greater than 2 and less than 10,000 (public)

Quick select: 23 29 31 37 41 47 53

Generator (g): A number between 2 and p-1 (public)

Note: In real-world systems, g must be a verified primitive root modulo p for security.

Alice's private key (a): Alice's secret number (1 to p-1)

Bob's private key (b): Bob's secret number (1 to p-1)

Step 1: Public Parameters

Both Alice and Bob agree on public parameters:

Prime (p) =
Generator (g) =

Step 2: Private Keys

Alice:

Private key (a) =

Bob:

Private key (b) =

Step 3: Public Key Generation

Alice calculates:

A = g^a mod p
A =
A =

Bob calculates:

B = g^b mod p
B =
B =

Step 4: Public Key Exchange

Alice → A = → Bob
Bob → B = → Alice

Step 5: Shared Secret Calculation