Fast In-Spectrum Graph Watermarks

TL;DR

This paper introduces FFG, a fast graph watermarking scheme that embeds watermarks in the Fourier transform of a graph's adjacency matrix, significantly reducing complexity while maintaining or improving performance.

Contribution

The paper presents FFG, a novel graph watermarking method inspired by image watermarking, with lower computational complexity and comparable or better effectiveness than existing methods.

Findings

FFG reduces watermarking complexity to O(N^2 log N).

FFG performs as well or better than state-of-the-art methods.

Embedding in Fourier domain enhances efficiency and robustness.

Abstract

We address the problem of watermarking graph objects, which consists in hiding information within them, to prove their origin. The two existing methods to watermark graphs use subgraph matching or graph isomorphism techniques, which are known to be intractable for large graphs. To reduce the operational complexity, we propose FFG, a new graph watermarking scheme adapted from an image watermarking scheme, since graphs and images can be represented as matrices. We analyze and compare FFG, whose novelty lies in embedding the watermark in the Fourier transform of the adjacency matrix of a graph. Our technique enjoys a much lower complexity than that of related works (i.e. in $\mathcal{O}\left(N^2 \log N\right)$), while performing better or at least as well as the two state-of-the-art methods.