Asian Journal of Physics Vol. 34, Nos 7 & 8 (2025) 415-428

Asymmetric optical cryptosystem using Helico-Conical beam speckles and Hessenberg decomposition in linear canonical transform domain

Harsh Vardhan1, Aswathi K Sivarajan1, Sakshi Choudharyl,2, Salla Gangi Reddy1, and Ravi Kumar1
1Department of Physics, SRM University-AP, Andhra Pradesh – 522 502, India
2Ben-Gurion University of the Negev, P. O. Box 653, Beer-Sheva 8410501, Israel
Dedicated to Prof Kehar Singh on the occasion of his 84th Birthday on July 3, 2025

The study presents a novel asymmetric optical cryptosystem for encoding a phase image by utilizing optical speckle patterns generated by scattering Helico-conical beam through ground glass plate. These speckle patterns are unique and extremely challenging to replicate because the physical process involved in generating them. The Hessenberg decomposition is used to produce the private key for decrypting the encoding data. Here, the input image is encoded as a phase image and then further modulated by Helico-conical beam speckle (HCBS) phase mask. The intermediate complex image is then processed using linear canonical transform (LCT) and Hessenberg decomposition to get the final encrypted image. The LCT has six independent parameters which expands the key space and improve robustness against the plaintext attack. The resilience of the technique is evaluated under several attacks, such as contamination attacks, known plaintext attacks (KPA), and chosen plaintext attacks (CPA). Numerical simulations are used to evaluate and confirm the proposed method effectiveness and validity. © Anita Publications. All rights reserved.
Doi: XXX
Keywords: Helico conical beam speckles (HCBS), Linear canonical transform (LCT), Hessenberg decomposition (HD).

Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
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References

  1. Wang X, Lin S, Xue J, Xu B, Chen J, Information security scheme using deep learning-assisted single-pixel imaging and orthogonal coding, Opt Express, 31(2023)2402–2413.
  2. Liu Q, Liang Y, Liu F, Yang X, Meng X, Optical image encryption based on singular value decomposition ghost imaging and fractional chaotic mapping, Opt Lasers Eng, 186(2025)108779; doi.org/10.1016/j.optlaseng.2024.108779 .
  3. Psaltis D, Coherent Optical Information Systems, Science, 298(2002)1359–1363.
  4. Refregier P, Javidi B, Optical image encryption based on input plane and Fourier plane random encoding, Opt Lett, 20(1995)767–769.
  5. Peng X, Zhang P, Wei H, Yu B, Known-plaintext attack on optical encryption based on double random phase keys, Opt Lett, 31(2006)1044–1046.
  6. Peng X, Wei H, Zhang P, Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain, Opt Lett, 31(2006)3261–3263.
  7. Chen W, Javidi B, Chen X, Advances in optical security systems, Adv Opt Photonics, 6(2014)120; doi.org/10.1364/AOP.6.000120.
  8. Unnikrishnan G, Joseph J, Singh K, Optical encryption by double-random phase encoding in the fractional Fourier domain, Opt Lett, 25(2000)887–889.
  9. Situ G, Zhang J, Double random-phase encoding in the Fresnel domain, Opt Lett, 29(2004)1584–1586.
  10. Tajahuerce E, Matoba O, Verrall S C, Javidi B, Optoelectronic information encryption with phase-shifting interferometry, Appl Opt, 39(2000)2313–2320.
  11. Qin W, Peng X, Asymmetric cryptosystem based on phase-truncated Fourier transforms, Opt Lett, 35(2010)118–120.
  12. Wang X, Zhao D, A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms, Opt Commun, 285(2012)1078–1081.
  13. Nishchal N K, Optical Cryptosystems, (IOP Publishing), 2019.
  14. Pérez-Cabré E, Abril H C, Millán M S, Javidi B, Photon-counting double-random-phase encoding for secure image verification and retrieval, J Opt (UK), 14(2012)094001; doi.org/10.1088/2040-8978/14/9/094001.
  15. Mehra I, Nishchal N K, Optical asymmetric image encryption using gyrator wavelet transform, Opt Commun, 354(2015)344–352.
  16. Jeon S H, Gil S K, Optical asymmetric cryptography modifying the RSA public-key protocol, Curr Opt Photon, 4(2020)103–114.
  17. Li W, Chang X, Yan A, Zhang H, Asymmetric multiple image elliptic curve cryptography, Opt Lasers Eng, 136(2021)106319; doi.org/10.1016/j.optlaseng.2020.106319.
  18. Yu N, Xi S, Wang X, Lang L, Wang X, Zhang L, Han H, Dong Z, Jiao X, Wang H, Optical implementation of image encryption based on digital holography and computer-generated hologram, J Opt, 22(2020)075702; doi: 10.1088/2040-8986/ab8ea0.
  19. Zhang Y, Wang B, Optical image encryption based on interference, Opt Lett, 33(2008)2443–2445.
  20. Sivarajan A K, Vardhan H, Choudhary S, Salla G, Kumar R, Asymmetric optical cryptosystem using C-point polarization singularity speckles and polar decomposition in 2D-NS-LCT domain, Phys Scr, 100(2025)055504; org/10.1088/1402-4896/adc49c.
  21. Vardhan H, Sivarajan A K, Sakshi, Reddy S G, Kumar R, Optical phase image encryption using Stokes parameters and singular value decomposition, J Opt, 26(2024)115701; doi.org/10.1088/2040-8986/ad77e2.
  22. Kumar R, Bhaduri B, Nishchal N K, Nonlinear QR code based optical image encryption using spiral phase transform, equal modulus decomposition and singular value decomposition, J Opt, 20(2018)015701; doi: 10.1088/2040-8986/aa9943.
  23. Mandapati V C, Vardhan H, Prabhakar S, Sakshi, Kumar R, Reddy S G, Singh R P, Singh K, Multi-user nonlinear optical cryptosystem based on polar decomposition and fractional vortex speckle patterns, Photonics, 10(2023)561; doi.org/10.3390/photonics10050561.
  24. Evans D J, Yalamov P, The Q Z orthogonal decomposition method, Parallel Algorithms and Applications, 2(1994)263–276.
  25. Vardhan H, Sakshi, Reddy S G, Muniraj I, Kumar R, A symmetric optical cryptosystem based on QZ decomposition and Hermite Gaussian beam speckles, Opt Quantum Electron, 56(2024)885; doi.org/10.1007/s11082-024-06740-w.
  26. Berry M V, Optical vortices evolving from helicoidal integer and fractional phase steps, J Opt A: Pure Appl Opt, 6(2004)259–268.
  27. Kumar P, Nishchal N K, Alfalou A, Controllable optical vortex array for image encoding, IEEE Photonics Technol Lett, 34(2022)521–524.
  28. Tian H, Zhuang X, Yan A, Zhang H, A novel multiple-image encryption with multi-petals structured light, Sci Rep, 14(2024)19559; doi.org/10.1038/s41598-024-70425-3.
  29. Shikder A, Kumar P, Nishchal N K, Image encryption by structured phase encoding and its effectiveness in turbulent medium, IEEE Photonics Technol Lett, 35(2023)128–131.
  30. Yang Q, Xie Z, Zhang M, Ouyang X, Xu Y, Cao Y, Wang S, Zhu L, Li X, Ultra-secure optical encryption based on tightly focused perfect optical vortex beams, Nanophotonics, 11(2022)1063–1070.
  31. Rao S K, Nishchal N K, AlFalou A, Optical asymmetric image encryption using vectorial light field encoding, Opt Commun, 554(2024)130097; doi.org/10.1016/j.optcom.2023.130097.
  32. Alonzo C A, Rodrigo P J, Glückstad J, Helico-conical optical beams: a product of helical and conical phase fronts, Opt Express, 13(2005)1749–1760.
  33. Su Q, Chen B, A novel blind color image watermarking using upper Hessenberg matrix, AEU-Int J Electron Commun, 78(2017)64–71.
  34. Liu J, Huang J, Luo Y, Cao L, Suyang, Wei D, Zhou R, An Optimized Image Watermarking Method Based on HD and SVD in DWT Domain, IEEE Access, 7(2019)80849–80860.
  35. Qasim I M, Mohammed E A, Optical image encryption based on linear canonical transform with sparse representation, Opt Commun, 533(2023)129262; doi.org/10.1016/j.optcom.2023.129262.
  36. Vanitha P, Manupati B, Muniraj I, Anamalamudi S, Salla G R, Singh R P, Augmenting data security: physical unclonable functions for linear canonical transform based cryptography, Appl Phys B, 128 (2022)183.
  37. Archana, Sachin, Singh P, Cascaded unequal modulus decomposition in Fresnel domain based cryptosystem to enhance the image security, Opt Lasers Eng, 137(2021)106399; doi.org/10.1016/j.optlaseng.2020.106399.
  38. Xu D, Duan S, Mao X, Ren W, Yao Y, Lin W, Zhang H, Liu B, Generation and reconfiguration of interference-pattern helico-conical beams, Chin Opt Lett, 22 (2024)090009; doi.org/10.3788/COL202422.090009.
  39. Kutay M A, Ozaktas H M, Rodrigo J A, Optical implementation of linear canonical transforms, Springer Series in Optical Sciences, 198(2016)179–194.

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