The Diffie–Hellman protocol

Setup. Public prime $p$ and primitive root $g$ mod $p$.

Protocol.
1. Alice picks secret $a$, sends $A=g^a\bmod p$ to Bob.
2. Bob picks secret $b$, sends $B=g^b\bmod p$ to Alice.
3. Alice computes $B^a=g^{ab}$; Bob computes $A^b=g^{ab}$. Shared key: $g^{ab}\bmod p$.

Security. An eavesdropper sees $p,g,A,B$ and must compute $g^{ab}$ from these, which requires solving the discrete logarithm problem (finding $a$ from $g^a$), believed to be hard.

Conclusion. Diffie–Hellman relies on modular arithmetic and the hardness of discrete logarithm.