Encoding watermark numbers as cographs using self-inverting permutations

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 extended the class of graphs which can be efficiently used in a software watermarking system by proposing an efficient codec system, i.e., encoding and decoding algorithms that embed/extract watermark values into/from cographs through the use of self-inverting permutations. More precisely, we present a codec system which takes as input an integer ω as watermark value, converts it into a self-inverting permutation π*, and then encodes the permutation π* as a cograph. The main property of our codec system is its ability to encode the same integer ω, using a self-inverting permutation π*, into more than one cograph. This property causes our system to be resilient to attacks since it can embed multiple copies of the same watermark number ω into an application program. Moreover, the proposed codec system has low time complexity and can be easily implemented.

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