Timothy G. Abbott

On the complexity of two-player win-lose games

The efficient computation of Nash equilibria is one of the most formidable challenges in computational complexity today. The problem remains open for two-player games. We show that the complexity of two-player Nash equilibria is unchanged when all outcomes are restricted to be 0 or 1. That is, win-or-lose games are as complex as the general case for two-player games.

Browser-based attacks on Tor

This paper describes a new attack on the anonymity of web browsing with Tor. The attack tricks a users web browser into sending a distinctive signal over the Tor network that can be detected using traffic analysis. It is delivered by a malicious exit node using a man-in-the-middle attack on HTTP. Both the attack and the traffic analysis can be performed by an adversary with limited resources. While the attack can only succeed if the attacker controls one of the victims entry guards, the method reduces the time required for a traffic analysis attack on Tor from O(nk) to O(n + k), where n is the number of exit nodes and k is the number of entry guards. This paper presents techniques that exploit the Tor exit policy system to greatly simplify the traffic analysis. The fundamental vulnerability exposed by this paper is not specific to Tor but rather to the problem of anonymous web browsing itself. This paper also describes a related attack on users who toggle the use of Tor with the popular Firefox extension Torbutton.

Hinged Dissections Exist

We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form any polygon in the collection. This result settles the open problem about the existence of hinged dissections between pairs of polygons that goes back implicitly to 1864 and has been studied extensively in the past ten years. Our result generalizes and indeed builds upon the result from 1814 that polygons have common dissections (without hinges). Our proofs are constructive, giving explicit algorithms in all cases. For two planar polygons whose vertices lie on a rational grid, both the number of pieces and the running time required by our construction are pseudopolynomial. This bound is the best possible, even for unhinged dissections. Hinged dissections have possible applications to reconfigurable robotics, programmable matter, and nanomanufacturing.

Hinged dissections exist

We prove that any finite collection of polygons of equal area has a common hinged dissection, that is, a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form any polygon in the collection. This result settles the open problem about the existence of hinged dissections between pairs of polygons that goes back implicitly to 1864 and has been studied extensively in the past ten years. Our result generalizes and indeed builds upon the result from 1814 that polygons have common dissections (without hinges). We also extend our result to edge-hinged dissections of solid 3D polyhedra that have a common (unhinged) dissection, as determined by Dehns 1900 solution to Hilberts Third Problem. Our proofs are constructive, giving explicit algorithms in all cases. For a constant number of planar polygons, both the number of pieces and running time required by our construction are pseudopolynomial. This bound is the best possible even for unhinged dissections. Hinged dissections have possible applications to reconfigurable robotics, programmable matter, and nanomanufacturing.