Instead of obsoleting RSA (or perhaps as well), I could tell the Machine to work on finding me a block cipher, a hash function and an asymmetric key scheme which have no computationally feasible attacks against them. But the trouble with that is, what would I do with them when I got back to the real world? I'm not a published cryptographer; how would I get people to believe my algorithms were better than those of any other random crank?

I think that I'd treat the claim of someone who had worked out how to factor big numbers cheaply with a certain amount of respect if they also claimed to have an unbreakable cypher. I suspect that might be good enough to get the big guns involved...