A dynamic watermarking model for embedding reducible permutation graphs into software

Software watermarking involves embedding a unique identifier or, equivalently, a watermark value, within a software to discourage software theft; towards the embedding process, several graph theoretic watermarking algorithmic techniques encode the watermark values as graph structures and embed them in application programs. Recently, we presented an efficient codec system for encoding a watermark number w as a reducible permutation graph F[π
^∗
] through the use of self-inverting permutations π
^∗
. In this paper, we propose a dynamic watermarking model for embedding the watermark graph F[π
^∗
] into an application program P. The main idea behind the proposed watermarking model is a systematic use of appropriate calls of specific functions of the program P. More precisely, our model uses the dynamic call-graph G(P, I
key
) of the program P, taken by the specific input I
key
, and the graph F[π
^∗
], and produces the watermarked program P
^∗
having the following key property: its dynamic call-graph G(P
^∗
, I
key
) and the reducible permutation graph F[π
^∗
] are isomorphic graphs. Within this idea the program P
^∗
is produced by only altering appropriate real-calls of specific functions of the input program P. Moreover, the proposed watermarking model incorporates such properties which cause it resilient to attacks.