Diffie-Hellman Example

Number Theory · Axiom Academy

EXAMPLE Diffie-Hellman Key Exchange A complete worked example of secure key exchange using modular arithmetic Excellent work! You've completed the Diffie-Hellman key exchange example. Here's what we learned: Public Parameters: Both parties agree on a prime p = 23 and generator g = 5 , which can be shared openly. Private Keys Stay Secret: Alice's private key a = 6 and Bob's private key b = 15 are never transmitted or shared. Public Exchange: Alice and Bob exchange public values A = 8 and B = 19 , which can be intercepted without compromising security. Shared Secret: Both parties compute the same shared secret s = 2 using their private key and the other's public value. Security Foundation: The security relies on the discrete logarithm problem - it's computationally hard to find a from g a mod p when p is large. In practice, much larger primes (hundreds of digits) are used to ensure security. This protocol forms the basis of secure key exchange in modern cryptography!

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