Diffie-Hellman

Diffie-Hellman is the key-agreement protocol, introduced in 1976 by Whitfield Diffie and Martin Hellman (New Directions in Cryptography), that lets two parties who share no prior secret compute a common key over a public channel. Each side publishes g raised to a private exponent modulo a large prime; both then raise the other's value to their own exponent to reach the same result, which an eavesdropper cannot derive without solving the discrete logarithm problem. It is the foundational key exchange behind TLS, IPsec, and SSH, most often in its elliptic-curve form X25519.

#Quantum vulnerability

Because Shor's algorithm computes discrete logarithms efficiently, a large quantum computer recovers the shared secret from the public values, breaking both finite-field and elliptic-curve Diffie-Hellman (Shor 1995). Post-quantum protocols therefore replace the interactive exchange with a key encapsulation mechanism such as ML-KEM, and current TLS deployments run Diffie-Hellman and ML-KEM together as hybrids.