Are there public key cryptography algorithms that are provably NP-hard to defeat? [closed]

Answer 1

This was an open question in 1998:

On the possibility of basing Cryptography on the assumption that P != NP by Oded Goldreich, Rehovot Israel, Shafi Goldwasser

From the abstract: "Our conclusion is that the question remains open".

--I wonder if that's changed in the last decade?

Edit:

As far as I can tell the question is still open, with recent progress toward an answer of no such algorithm exists.

Adi Akavia, Oded Goldreich, Shafi Goldwasser, and Dana Moshkovitz published this paper in the ACM in 2006: On basing one-way functions on NP-hardness "Our main findings are the following two negative results"

The stanford site Complexity Zoo is helpful in decripting what those two negative results mean.