Design and Evaluation of a Graph Codec System for Software Watermarking

In this paper, we propose an efficient and easily implemented codec system for encoding watermark numbers as graph structures thought the use of self-inverting permutations. More precisely, based on the fact that a watermark number w can be efficiently encoded as self-inverting permutation π∗, we present an efficient encoding algorithm which encodes a self-inverting permutation π∗ as a reducible flow-graph F [π∗] and a decoding algorithm which extracts the permutation π∗ from the graph F [π∗]. Our codec algorithms are very simple, use elementary operations on sequences and linked structures, and the produced flow-graph F [π∗] does not differ from the graph data structures built by real programs. Moreover, our codec algorithms have very low time and space complexity and the flow-graph F [π∗] incorporates important structural properties which cause it resilient to attacks. We have evaluated several components of our codec system in a simulation environment in order to obtain a clear view of their practical behaviour; the experimental results show that we can decide with high probability whether the graph F [π∗] suffer an attack on its edges.