Examples of NP Complete key exchange algorithms
There are no known public-key cryptographic algorithms that have been proven to be NP-hard to break.  None.  So we can't provide you examples, because none are known.



Answer to your original question:

The analysis at Why hasn&#39;t there been an encryption algorithm that is based on the known NP-Hard problems? also applies to public-key exchange.

Cryptography requires average-case hardness.  NP-hardness relates to worst-case hardness; it has no notion of a distribution on inputs, probability, or any kind of "average".  Worst-case hardness does not appear to imply average-case hardness: there are many problems that are believed to be hard in the worst case, but easy in the average case. Status of Impagliazzo's Worlds?
 has some pointers on this topic.