Two RPG Flow-graphs for Software Watermarking using Bitonic Sequences of Self-inverting Permutations

TL;DR

This paper introduces two new reducible permutation flow-graphs based on bitonic subsequences of self-inverting permutations, enhancing software watermarking techniques by allowing multiple embeddings and improved resilience against attacks.

Contribution

The paper extends existing watermark encoding methods by proposing two novel flow-graphs that encode self-inverting permutations, increasing flexibility and robustness in software watermarking.

Findings

Efficient encoding and decoding of self-inverting permutations into the new flow-graphs.

Multiple graph structures for the same watermark number enable redundancy.

Enhanced resilience of watermarking against attacks due to graph variety.

Abstract

Software watermarking has received considerable attention and was adopted by the software development community as a technique to prevent or discourage software piracy and copyright infringement. A wide range of software watermarking techniques has been proposed among which the graph-based methods that encode watermarks as graph structures. Following up on our recently proposed methods for encoding watermark numbers $w$ as reducible permutation flow-graphs $F[\pi^*]$ through the use of self-inverting permutations $\pi^*$, in this paper, we extend the types of flow-graphs available for software watermarking by proposing two different reducible permutation flow-graphs $F_1[\pi^*]$ and $F_2[\pi^*]$ incorporating important properties which are derived from the bitonic subsequences composing the self-inverting permutation $\pi^*$. We show that a self-inverting permutation $\pi^*$ can be efficiently encoded into either $F_1[\pi^*]$ or $F_2[\pi^*]$ and also efficiently decoded from theses graph structures. The proposed flow-graphs $F_1[\pi^*]$ and $F_2[\pi^*]$ enrich the repository of graphs which can encode the same watermark number $w$ and, thus, enable us to embed multiple copies of the same watermark $w$ into an application program $P$. Moreover, the enrichment of that repository with new flow-graphs increases our ability to select a graph structure more similar to the structure of a given application program $P$ thereby enhancing the resilience of our codec system to attacks.