A Graph Theoretic Approach to Software Watermarking

Abstract

We present a graph theoretic approach for watermarking software in a robust fashion. While watermarking software that are small in size (e.g. a few kilobytes) may be infeasible through this approach, it seems to be a viable scheme for large applications. Our approach works with control/data flow graphs and uses abstractions, approximate k-partitions, and a random walk method to embed the watermark, with the goal of minimizing and controlling the additions to be made for embedding, while keeping the estimated effort to undo the watermark (WM) as high as possible. The watermarks are so embedded that small changes to the software or flow graph are unlikely to disable detection by a probabilistic algorithm that has a secret. This is done by using some relatively robust graph properties and error correcting codes.

Under some natural assumptions about the code added to embed the WM, locating the WM by an attacker is related to some graph approximation problems. Since little theoretical foundation exists for hardness of typical instances of graph approximation problems, we present heuristics to generate such hard instances and, in a limited case, present a heuristic analysis of how hard it is to separate the WM in an information theoretic model. We describe some related experimental work. The approach and methods described here also suitable for solving the problem of software tamper resistance.