Editor-in-Chief : V.K. Rastogi

Asian Journal of Physics | Vol 32, Nos 3 & 4 (2023) A11-A24 |

**An asymmetric hybrid image encryption algorithm using fractional Hartley transform, Bird Wings Map, and embedded watermarking**

DJoyti^{1}, Sachin^{2}, Phool Singh^{3}, and Kehar Singh^{4}^{1}Department of Mathematics, Government College Barota, Gohana, Haryana-131 301, India^{2}Department of Mathematics, IIHS, Kurukshetra University, Kurukshetra, Haryana-136 119, India^{3}Department of Mathematics, SOET, Central University of Haryana, Mahendergarh-123 031, India^{4}Optics and Photonics Center, Indian Institute of Technology Delhi, New Delhi-110 016, India*Dedicated to Prof Jay M Enoch*

We present an improved security algorithm based on fractional Hartley transform, phase truncation and phase reservation, newly developed ‘Bird Wings Map’(BWM), and watermarking. The BWM enhances security of the proposed algorithm by providing additional parameters to the cryptosystem. The effectiveness of the scheme is validated through simulations conducted on a pair of grayscale images, namely Cameraman and Baboon. The Cameraman is used as the target image, while the Baboon serves as the host image in the watermarking process. The proposed scheme is tested against various statistical attacks, using mean-squared-error, correlation coefficient, information entropy, and peak signal-to-noise ratio. Additionally, the histogram and mesh plots are also provided. Real-time attacks such as noise-, and occlusion attacks are also applied to validate the robustness of the proposed scheme. Furthermore, the strength of the scheme is tested against the well-known attacks, such as known-plaintext-, chosen-plaintext-, and special iterative attack. Key sensitivity analysis is performed to analyze the key-space of the proposed scheme. The simulation results demonstrate the robustness and effectiveness of the scheme which exhibits resilience against the statistical attacks, real-time attacks, and cryptographic attacks. © Anita Publications. All rights reserved.**Keywords**: Asymmetric image encryption, Fractional Hartley transform, Phase truncation and phase reservation, Bird Wings Map, Watermarking, Key sensitivity.

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