Antibodies

Antibodies by Charles Stross

This short story was first published in 2000, and later published in the compilation Toast: And Other Rusted Futures. A mathematician publishes a paper that solves the traveling salesman problem and transforms NP-complete problems to easily solvable ones. This seemingly breaks all cryptography. The story them picots to AIs gone amok. The AI has grown and taken on an identity of its own. It has started to consume all electronic resources and then goes on to inhabit the real world. A couple is trying to reach an "extraction point" where they can escape from this world. Alas, they are caught a little before escaping. Luckily, they appear to have "anitbodies" and are able to escape. There are a few interesting concepts in this story, but they don't quite come together.