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.