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An asymmetric optical watermarking method based on Schur decomposition and Laguerre-Gaussian beam speckles

Year : 2026

Publisher : Elsevier B.V.

Source Title : Optics Communications

Document Type :

Abstract

This study presents a new robust asymmetric optical watermarking scheme using Schur decomposition and the Laguerre-Gaussian (LG) beam speckles as security keys. A LG beam with a nonzero azimuthal index possesses orbital angular momentum (OAM) and has a donut-shaped intensity profile having helical phase structure, characterized by radial (p) and azimuthal (l) indices. Owing to their orthogonality and OAM characteristic, LG beam possesses potential applications in optical information security. We have scattered LG beams of different indices through a diffuser to synthesize the distinctive encryption keys. The obtained speckle patterns are unique and nearly impossible to duplicate, as they are generated through physical process. Here, we propose a watermarking technique in which the input plaintext image is first phase encoded followed by modulation with the encryption key synthesized from LG beam speckles. Afterwards, the obtained complex wavefront is Fresnel propagated over a distance d 1 and the output is modulated with another encryption key, followed by Schur decomposition to make the system asymmetric and to generate the private key. Furthermore, the processed part is again modulated with third encryption key, and an Improved ZigZag sequence is utilized to enhance the randomness in the system, which helps in boost the security. Then the resulting wavefront is propagated to distance d 2 and embedded into a host image to get the final watermarked image. The efficacy of the proposed technique is examined against multiple established attacks, including contamination attacks, chosen plaintext attacks, and known plaintext attacks.