Hiding Signatures in Graph Coloring Solutions

Abstract. One way to protect a digital product is to embed an author's signature into the object in the form of minute errors. However, this technique cannot be directly applied to protect intellectual properties such as solutions to hard problems which must maintain the correct functionality. This paper proposes a constraint-based watermarking technique and lays out a theoretical framework to evaluate this type of technique. Based on this framework, we analyze three watermarking techniques for the graph coloring problem because of its theoretical importance in complexity theory and numerous applications in real life. The rst adds extra edges between some pairs of vertices and therefore forces them to be colored by di erent colors. The second pre-colors a set of well-selected vertices according to the watermark. And the last introduces new vertices and edges to the graph. Since credibility and overhead are the most important criteria for any e cient watermarking technique, we deri...

• Type: Conference
• Year: 1999
• Where: IH
• Authors: Gang Qu, Miodrag Potkonjak
• Keywords: Constraint-based Watermarking Technique, IH 1999, Information Management, Random Graphs, Watermarking Techniques