Experimental Study of the Resilience of a Graph-based Watermarking System under Edge Modifications

Abstract

Over the last 25 years, a wide range of software watermarking techniques has been proposed encoding watermark numbers as graphs whose structure resembles that of real program graphs. In this domain, we have recently proposed several watermarking codec systems for encoding integer numbers w as reducible permutation flow-graphs F[π*] through the use of self-inverting permutations π*. Following up on our codec systems, we experimentally study the oldest one in order to investigate and attest its resilience to edge-modification attacks on its flow-graph F[π*]. In particular, we construct the flow-graphs F[πi*] which encode the watermarks wi in the range R4 = [8,15], we attack the graph F[πi*] by modifying k edges, perform a series of experiments for each attack case, and determine the percentage of the cases maintaining four properties, namely, Odd-One, Bitonic, Block and Range. Whenever a flow-graph F[πi*] is attacked having k edges modified, if all the four properties are satisfied during the decoding process then the decoding algorithm returns a true-incorrect watermark wj, that is, wj ≠ wi. The experimental study reveals those watermarks wi ∈ R4 which are more resilient in the sense that the decoding algorithm has low probability to return a true-incorrect watermark wj after an edge-modification attack to graph F[πi*] encoding a watermark wi.