Abstract
The paper presents a methodology to protect the integrity of multichannel images, having some highly redundant channels, by means of a reversible fragile watermarking algorithm. The watermark embedding phase uses a lossless compression method to compress the high redundancy channels, stores the compressed stream into their most significant bits, then embeds a secret fragile watermark by modifying the least significant bits of the high redundancy channels. In case the watermarked image is not modified, the host image can be perfectly reconstructed; otherwise, the modified area can be detected and located with very high probability and the area that has not been forged can be restored as in the original host image. The embedding of the watermark is performed by a Genetic Algorithm in the Karhunen-Loève Transform (KLT) domain: the use of a secret space defined by the KLT guarantees both security of the method and a high sensitivity in the detection of the forged areas.
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Notes
For simplicity of the discussion we assume that both H and W are multiples of n.
The computational complexity of this step depends on the complexity of the SHA-3 algorithm.
We designed an experimental setting in which we test how many times the verifier misses a tampered subimage when a single pixel of that subimage is changed by just 1 or 2 grey levels. This is actually the smallest tampering an attacker can perform: any other attack, such as filtering, blurring, noise addition, copy-and-paste, cropping, etc., would modify more pixels and, very likely, of more than just 1 grey level.
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Acknowledgements
We would like to thank Dr. Roberto Esposito who helped in revising the manuscript according to the reviewers’ comments and making new experiments, pointing out and resolving issues in the first submission.
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Botta, M., Cavagnino, D. & Pomponiu, V. Reversible Fragile Watermarking for Multichannel Images with High Redundancy Channels. Multimed Tools Appl 79, 26427–26445 (2020). https://doi.org/10.1007/s11042-020-08986-4
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DOI: https://doi.org/10.1007/s11042-020-08986-4