Multiple encoding of a watermark number into reducible permutation graphs using cotrees
Proceedings of the 13th International Conference on Computer Systems and Technologies
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In a software watermarking environment, several graph theoretic watermark methods encode the watermark values as graph structures and embed them in application programs. In this paper we first present an efficient codec system for encoding a watermark number $w$ as a reducible permutation graph $F[\pi^*]$ through the use of the self-inverting permutation $\pi^*$ which encodes the number $w$ and, then, we propose a method for embedding the watermark graph $F[\pi^*]$ into a program $P$. The main idea behind the proposed embedding method is a systematic use of appropriate calls of specific functions of the program $P$. That is, our method embeds the graph $F[\pi^*]$ into $P$ using only real functions and thus the size of the watermarked program $P^*$ remains very small. Moreover, the proposed codec system has low time complexity, can be easily implemented, and incorporates such properties which cause it resilient to attacks.