Volume 15, Issue 6

A Secure Multi – Image Optical Encryption Scheme Based on Quasi – Zernike Synthesis, Cascaded Equal Modulus Decomposition, and the Gyrator Transform

Author

Ajay Singh and Nagander Singh Tomer

Abstract

The widespread transmission and storage of digital images over open communication networks have made secure image encryption an essential research topic. Although numerous optical encryption techniques have been reported, many existing methods are constrained by limited key diversity, insufficient resistance to cryptanalytic attacks, and reduced robustness under adverse transmission conditions. This paper proposes a multi – image encryption framework by integrating Quasi – Zernike (QZ) synthesis, the gyrator transform (GT), random phase mask (RPMs), and equal modulus decomposition (EMD). Initially, two plaintext images are fused using QZ synthesis to generate multiple private keys. The synthesized output is then combined with a phase image and encrypted through dual GT operations interleaved with RPM modulation and EMD, producing additional secret keys and a highly randomized ciphertext. The original images are recovered by performing the inverse operations using the corresponding private keys. The effectiveness of the proposed framework is validated through CC, MSE, PSNR, SSIM, information entropy, histogram, pixel correlation, and key sensitivity analyses, together with brute – force, noise and occlusion attack evaluations. Experimental results demonstrate near – lossless image reconstruction, high ciphertext randomness, and strong robustness against statistical and differential attacks. The proposed framework offers a secure and efficient solution for optical multi – image encryption and protected image communication.

Keywords: Multi – image encryption, Gyrator transform, Quasinormal – Zernike algorithm, Equal Modulus Decomposition.

Reference:

[1]     P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett., vol. 20, no. 7, pp. 767–769, Apr. 1995, doi: 10.1364/OL.20.000767.

[2]     R. Girija and H. Singh, “A cryptosystem based on deterministic phase masks and fractional Fourier transform deploying singular value decomposition,” Opt Quant Electron, vol. 50, no. 5, Art. no. 5, May 2018, doi: 10.1007/s11082-018-1472-6.

[3]     P. Singh, A. K. Yadav, K. Singh, and I. Saini, “Optical image encryption in the fractional Hartley domain, using Arnold transform and singular value decomposition,” AIP Conference Proceedings, vol. 1802, no. 1, pp. 020017-1–7, Jan. 2017, doi: 10.1063/1.4973267.

[4]     H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, “Optical image encryption using devil’s vortex toroidal lens in the Fresnel transform domain,” International Journal of Optics, vol. 2015, pp. 1–13, 2015, doi: 10.1155/2015/926135.

[5]     Anshula and H. Singh, “Cryptanalysis for double-image encryption using the DTLM in frequency plane with QR decomposition and gyrator transform,” Opt Rev, vol. 28, no. 6, pp. 596–610, Dec. 2021, doi: 10.1007/s10043-021-00705-0.

[6]     H. Singh, “Hybrid structured phase mask in frequency plane for optical double image encryption in gyrator transform domain,” Journal of Modern Optics, vol. 0, no. 0, pp. 1–14, Jul. 2018, doi: 10.1080/09500340.2018.1496286.

[7]     M. R. Abuturab, “An asymmetric single-channel color image encryption based on Hartley transform and Gyrator transform,” Optics and Lasers in Engineering, vol. 69, pp. 49–57, Jun. 2015, doi: 10.1016/j.optlaseng.2015.01.001.

[8]     A. Lopez-Caloca and B. Escalante-Ramirez, “The Hermite Transform: An Efficient Tool for Noise Reduction and Image Fusion in Remote-Sensing,” in Image Processing for Remote Sensing, C. Chen, Ed., CRC Press, 2007, pp. 273–291. Accessed: Mar. 21, 2020. [Online]. Available: http://www.crcnetbase.com/doi/10.1201/9781420066654.ch12

[9]     Shalu, A. K. Yadav, and P. Singh, “Uniquely designed optical cryptosystem for watermarking of double-color images in the fractional Hermite-transform domain,” Opt. Eng., vol. 64, no. 09, Sep. 2025, doi: 10.1117/1.OE.64.9.093101.

[10]   Shalu, P. Singh, and A. K. Yadav, “Watermarking based on asymmetric dual-image encryption using QZ algorithm and vortex toroidal lenses in fractional Hermite transform domain,” Optik, vol. 342–343, p. 172598, Dec. 2025, doi: 10.1016/j.ijleo.2025.172598.

[11]   P. Rakheja, R. Vig, and P. Singh, “Asymmetric hybrid encryption scheme based on modified equal modulus decomposition in hybrid multi-resolution wavelet domain,” Journal of Modern Optics, vol. 66, no. 7, pp. 799–811, Apr. 2019, doi: 10.1080/09500340.2019.1574037.

[12]   M. Agoyi, E. Çelebi, and G. Anbarjafari, “A watermarking algorithm based on chirp z-transform, discrete wavelet transform, and singular value decomposition,” SIViP, vol. 9, no. 3, pp. 735–745, Mar. 2015, doi: 10.1007/s11760-014-0624-9.

[13]   P. Singh, A. K. Yadav, and K. Singh, “Known-Plaintext Attack on Cryptosystem Based on Fractional Hartley Transform Using Particle Swarm Optimization Algorithm,” in Engineering Vibration, Communication and Information Processing, vol. 478, K. Ray, S. N. Sharan, S. Rawat, S. K. Jain, S. Srivastava, and A. Bandyopadhyay, Eds., Singapore: Springer Singapore, 2019, pp. 317–327. doi: 10.1007/978-981-13-1642-5_29.

[14]   X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Optics letters, vol. 31, no. 22, pp. 3261–3263, Nov. 2006, doi: 10.1364/OL.31.003261.

[15]   A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Optics letters, vol. 30, no. 13, pp. 1644–1646, 2005, doi: https://doi.org/10.1364/OL.30.001644.

[16]   S. Jiao, G. Li, C. Zhou, W. Zou, and X. Li, “Special ciphertext-only attack to double random phase encryption by plaintext shifting with speckle correlation,” J. Opt. Soc. Am. A, JOSAA, vol. 35, no. 1, pp. A1–A6, Jan. 2018, doi: 10.1364/JOSAA.35.0000A1.

[17]   W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Optics letters, vol. 35, no. 2, pp. 118–120, Jan. 2010, doi: 10.1364/OL.35.000118.

[18]   J. Cai, X. Shen, M. Lei, C. Lin, and S. Dou, “Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition,” Optics letters, vol. 40, no. 4, pp. 475–478, Feb. 2015, doi: 10.1364/OL.40.000475.

[19]   Archana, P. Singh, and P. Rakheja, “Asymmetric watermarking scheme for color images using cascaded unequal modulus decomposition in Fourier domain,” Journal of Modern Optics, vol. 68, no. 20, pp. 1094–1107, Nov. 2021, doi: 10.1080/09500340.2021.1977404.

[20]   Sachin, P. Singh, R. Kumar, and A. K. Yadav, “Asymmetric cryptosystem for color images based on unequal modulus decomposition in Chirp-z domain,” in Proceedings of Academia-Industry Consortium for Data Science, G. Gupta, L. Wang, A. Yadav, P. Rana, and Z. Wang, Eds., in Advances in Intelligent Systems and Computing, vol. 1411. Singapore: Springer Nature, 2022, pp. 331–344. doi: 10.1007/978-981-16-6887-6_27.

[21]   R. Yadav and P. Singh, “Asymmetric image authentication algorithm using double random modulus decomposition and CGI,” Computational and Applied Mathematics, vol. 42, no. 7, p. 305, Sep. 2023, doi: 10.1007/s40314-023-02443-2.

[22]   S. Anjana, A. Yadav, P. Singh, and H. Singh, “Audio and image encryption scheme based on QR decomposition and random modulus decomposition in Fresnel domain,” Optica Applicata, vol. 52, no. 3, pp. 359–374, 2022, doi: 10.37190/oa220303.

[23]   P. Singh, A. K. Yadav, and K. Singh, “Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition,” Optics and Lasers in Engineering, vol. 91, pp. 187–195, Apr. 2017, doi: 10.1016/j.optlaseng.2016.11.022.

[24]   P. Singh, A. K. Yadav, and K. Singh, “Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition,” Optics and Lasers in Engineering, vol. 91, pp. 187–195, Apr. 2017, doi: 10.1016/j.optlaseng.2016.11.022.

[25]   Q. Su, G. Wang, G. Lv, X. Zhang, G. Deng, and B. Chen, “A novel blind color image watermarking based on Contourlet transform and Hessenberg decomposition,” Multimed Tools Appl, vol. 76, no. 6, pp. 8781–8801, Mar. 2017, doi: 10.1007/s11042-016-3522-z.

[26]   Anshula and H. Singh, “Cryptanalysis for double-image encryption using the DTLM in frequency plane with QR decomposition and gyrator transform,” Opt Rev, vol. 28, no. 6, pp. 596–610, Dec. 2021, doi: 10.1007/s10043-021-00705-0.

[27]   P. Rakheja, P. Singh, and R. Vig, “An asymmetric image encryption mechanism using QR decomposition in hybrid multi-resolution wavelet domain,” Optics and Lasers in Engineering, vol. 134, p. 106177, Nov. 2020, doi: 10.1016/j.optlaseng.2020.106177.

[28]   R. Yadav, Sachin, and P. Singh, “Multidomain asymmetric image encryption using phase-only CGH, QZS method and Umbrella map,” J Opt, Aug. 2024, doi: 10.1007/s12596-024-02106-3.

[29]   M. R. Abuturab, “An asymmetric color image cryptosystem based on Schur decomposition in gyrator transform domain,” Optics and Lasers in Engineering, vol. 58, pp. 39–47, Jul. 2014, doi: 10.1016/j.optlaseng.2014.01.025.

[30]   Sachin, Archana, and P. Singh, “Optical image encryption algorithm based on chaotic Tinkerbell map with random phase masks in Fourier domain,” in Proceedings of International Conference on Data Science and Applications, K. Ray, K. C. Roy, S. K. Toshniwal, H. Sharma, and A. Bandyopadhyay, Eds., in Lecture Notes in Networks and Systems, vol. 148. Singapore: Springer, 2021, pp. 249–262. doi: 10.1007/978-981-15-7561-7_20.

[31]   Sachin and P. Singh, “A novel chaotic Umbrella map and its application to image encryption,” Opt Quant Electron, vol. 54, no. 5, p. 266, Apr. 2022, doi: 10.1007/s11082-022-03646-3.

[32]   P. Rakheja, S. Yadav, and A. Tobria, “A novel image encryption mechanism based on umbrella map and Yang-Gu algorithm,” Optik, vol. 271, p. 170152, Dec. 2022, doi: 10.1016/j.ijleo.2022.170152.

[33]   Archana, Sachin, and P. Singh, “Cryptosystem based on triple random phase encoding with chaotic Henon map,” in Proceedings of International Conference on Data Science and Applications, vol. 148, K. Ray, K. C. Roy, S. K. Toshniwal, H. Sharma, and A. Bandyopadhyay, Eds., Singapore: Springer Singapore, 2021, pp. 73–84. Accessed: Jan. 03, 2021. [Online]. Available: http://link.springer.com/10.1007/978-981-15-7561-7_5

[34]   Sachin and P. Singh, “Analysis of chaotic patterns in the Bird wing map and implications in image security,” Journal of Modern Optics, vol. 0, no. 0, pp. 1–26, Jul. 2025, doi: 10.1080/09500340.2025.2508790.

[35]   P. Singh, A. K. Yadav, K. Singh, and I. Saini, “Optical image encryption in the fractional Hartley domain, using Arnold transform and singular value decomposition,” AIP Conference Proceedings, vol. 1802, no. 1, pp. 020017-1–7, Jan. 2017, doi: 10.1063/1.4973267.

[36]   J. Cai, X. Shen, and C. Lin, “Security-enhanced asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition,” Opt. Commun., vol. 359, pp. 26–30, Jan. 2016, doi: 10.1016/j.optcom.2015.09.058.

[37]   S. P. Barfungpa and M. R. Abuturab, “Asymmetric cryptosystem using coherent superposition and equal modulus decomposition of fractional Fourier spectrum,” Opt Quant Electron, vol. 48, no. 11, Art. no. 11, Nov. 2016, doi: 10.1007/s11082-016-0786-5.

[38]   H. Singh and K. Singh, “A watermarking-based asymmetric cryptosystem using gyrator transform, QZ modulation, and fractional vortex toroidal phase mask,” J Opt, vol. 54, no. 2, pp. 300–313, Apr. 2025, doi: 10.1007/s12596-024-02329-4.

[39]   R. Yadav, Sachin, and P. Singh, “Multidomain asymmetric image encryption using phase-only CGH, QZS method and Umbrella map,” J Opt, pp. 1–18, Aug. 2024, doi: 10.1007/s12596-024-02106-3.

[40]   M. R. Abuturab, “Color information verification system based on singular value decomposition in gyrator transform domains,” Optics and Lasers in Engineering, vol. 57, pp. 13–19, Jun. 2014, doi: 10.1016/j.optlaseng.2014.01.006.

[41]   J. Kumar, P. Singh, A. K. Yadav, and A. Kumar, “Asymmetric Image Encryption Using Gyrator Transform with Singular Value Decomposition,” in Engineering Vibration, Communication and Information Processing, vol. 478, K. Ray, S. N. Sharan, S. Rawat, S. K. Jain, S. Srivastava, and A. Bandyopadhyay, Eds., Singapore: Springer Singapore, 2019, pp. 375–383. doi: 10.1007/978-981-13-1642-5_34.

[42]   S. P. Barfungpa and M. R. Abuturab, “Asymmetric cryptosystem using coherent superposition and equal modulus decomposition of fractional Fourier spectrum,” Opt Quant Electron, vol. 48, no. 11, Art. no. 11, Nov. 2016, doi: 10.1007/s11082-016-0786-5.

DOI

https://doi.org/10.62226/ijarst20262724

PAGES : 2142-2152 | 6 VIEWS | 2 DOWNLOADS


Download Full Article

Ajay Singh and Nagander Singh Tomer | A Secure Multi – Image Optical Encryption Scheme Based on Quasi – Zernike Synthesis, Cascaded Equal Modulus Decomposition, and the Gyrator Transform | DOI : https://doi.org/10.62226/ijarst20262724

Journal Frequency: ISSN 2320-1126, Monthly
Paper Submission: Throughout the month
Acceptance Notification: Within 6 days
Subject Areas: Engineering, Science & Technology
Publishing Model: Open Access
Publication Fee: USD 60  USD 50
Publication Impact Factor: 6.76
Certificate Delivery: Digital

Publish your research with IJARST and engage with global scientific minds