The Evolution of Diffie-Hellman Hard Problems

So who has made the greatest contribution to Cybersecurity? Well, possibly it is Whitfield Diffie and Martin Hellman and who, in 1976, published their classic paper [here]:

Since then most secure connections we make over the Internet involves some form of their original method, and where Bob and Alice can determine the same encryption key, without anyone else finding it out. It all started with discrete logs, and where the Diffie-Hellman method defined:

Alice generates a, Bob generates b.

Alice passes g^a, and Bob passes g^b. They then calculated the shared secret of g^{ab}.

The hard problem is:

Given g, and g^x, it is difficult to find x. [here]

We then advanced to ECDH (Elliptic Curve Diffie Hellman), and where we have a base point (P).

Alice generates a, Bob generates b.

Alice passes aP and Bob passes bP. They then calculate the shared secret of abP. The hard problem is:

Given P, and xP, it is difficult to find x. [here]