Towards a provably resilient scheme for graph-based watermarking

TL;DR

This paper extends and formalizes a graph-based digital watermarking scheme, proving its resilience to edge removals and providing algorithms for watermark recovery, thus enhancing its robustness for software piracy prevention.

Contribution

It offers a formal graph characterization, a linear-time recovery algorithm for up to two edge removals, and a simplified decoding method for arbitrary edge losses.

Findings

Proved the scheme withstands up to two edge removals.

Developed a linear-time algorithm for watermark recovery.

Provided a simplified decoding function for arbitrary edge loss.

Abstract

Digital watermarks have been considered a promising way to fight software piracy. Graph-based watermarking schemes encode authorship/ownership data as control-flow graph of dummy code. In 2012, Chroni and Nikolopoulos developed an ingenious such scheme which was claimed to withstand attacks in the form of a single edge removal. We extend the work of those authors in various aspects. First, we give a formal characterization of the class of graphs generated by their encoding function. Then, we formulate a linear-time algorithm which recovers from ill-intentioned removals of $k \leq 2$ edges, therefore proving their claim. Furthermore, we provide a simpler decoding function and an algorithm to restore watermarks with an arbitrary number of missing edges whenever at all possible. By disclosing and improving upon the resilience of Chroni and Nikolopoulos's watermark, our results reinforce the interest in regarding it as a possible solution to numerous applications.