Security · interactive
Key exchange: Diffie-Hellman
Alice and Bob want a shared secret key, but everything they send can be read by Eve. Each picks a private number, sends a public one, and both end up with the same secret that never crossed the wire. Tiny numbers here so you can check the maths.
public: p = 23, g = 5
Alice
secret a = 6
A = 5^6 mod 23 = 8
B^a mod p = 2
Eve sees
p = 23, g = 5
A = 8, B = 19
not a, b, or the secret
Bob
secret b = 15
B = 5^15 mod 23 = 19
A^b mod p = 2
shared secret: 2 = 2
Eve could try every a until 5^a mod 23 = 8: she finds a = 6 in 6 tries. With a 2048-bit p that search takes longer than the age of the universe.
Both compute g^(ab) mod p = 2: Alice as (g^b)^a, Bob as (g^a)^b. Eve only has g^a and g^b, and multiplying those gives g^(a+b), not g^(ab).
1 2 3 Each raises the other's public value to their own secret. The results match; derive the session key from it.
(g^b)^a = (g^a)^b
4
In production
Tools and technologies
Every TLS connection starts with a key exchange.
Not tied to one language — use these names when you search docs or design a system.