Submit Article

Asian Journal of Physics Vol. 33, Nos 3 & 4 (2024) 269-286

A secure image encryption method using toroidal vortex phase masks, QR decomposition, and gyrator transform

Hukum Singh1 and Kehar Singh1,2
1Department of Applied Sciences, The NorthCap University, Gurugram-122 017, India
2Optics and Photonics Center, Indian Institute of Technology Delhi, New Delhi-110 016, India

Dedicated to Professor Anna Consortini for her significant contributions and pioneering works in the field of atmospheric turbulence and her continuous commitment to promote optics at global level 

This paper introduces a security-enhanced hybrid image encryption method that employs toroidal vortex phase masks (TVPMs) and QR decomposition, with gyrator transform. The TVPMs used are intricate phase masks created by combining the phases of radial Hilbert transform (RHT) and the toroidal zone plate (TZP). The QR decomposition, a mathematical operation, is employed for matrix decomposition, serving as a replacement for the conventional phase-truncated Fourier transform (PTFT) method. The cryptosystem exhibits asymmetry, given that the encryption and decryption procedures are not the same as they rely on different sets of security keys. The keys produced during the encryption are utilized in the decoding system to retrieve the input image. System performance is tested by evaluating the mean-square error, peak signal-to-noise ratio, key sensitivity, cropping effect, correlation coefficients, 3-D mesh, histograms, and noise-attacks. © Anita Publications. All rights reserved.
Doi: 10.54955/AJP.33.3-4.2024.269-286
Keywords: Gyrator transform, Toroidal phase mask, Hilbert transform, QR decomposition, Performance evaluation.

Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserve

References

  1. Refregier P, Javidi B, Optical image encryption based on input plane and Fourier plane random encoding, Opt Lett, 20(1995)767–769.
  2. Singh K, Unnikrishnan G, Nishchal N K, Photorefractive optical processing for data security, In, Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications, VII, Proc SPIE 4803(2002)205–219.
  3. Javidi B (ed), Optical and Digital Techniques for Information Security, (Springer New York USA), 2005.
  4. Naughton T J, Sheridan J T, Optics in information systems, SPIE Int Techn Group News Lett, 16(2005)1–12.
  5. Singh K, John R, Joseph Encrypted holographic memories for information security, Bull Laser Spectrosc Soc (India), 15(2005-6)1–19.
  6. Matoba O, Nomura T, Perez-Cabre E, Millan M S, Javidi B, Optical techniques for information security, Proc IEEE, 97(2009)1128–1148.
  7. Alfalou A, Brosseau C, Optical image compression and encryption methods, Adv Opt Photon, 1(2009)589–536.
  8. Millan M S, Perez-Cabre E, Optical data encryption, In Optical and Digital Image Processing: Fundamentals and Applications, Cristobal G, Schelkens P, Thienpont H (eds), (Wiley N Y), 2011, pp 739–767. .
  9. Kumar A, Singh M, Singh K, Speckle coding for optical and digital data security applications, In Advances in Speckle Metrology and Related Techniques, (ed) Kaufmann G, Chap 6, (Wiley-VCH Weinheim, Germany), 2011, pp 239–299.
  10. Liu S, Guo C, Sheridan J T, A review of optical image encryption techniques, Opt Laser Technol,57(2014)327–342.
  11. Chen W, Javidi B, Chen X, Advances in optical security systems, Adv Opt Photon, 6(2014)120–155.
  12. Yadav A K, Vashisth S, Singh H, Singh K, Optical cryptography and watermarking using some fractional canonical transforms and structured masks, in Advances in Optical Science and Engineering, (eds) Lakshminarayanan V, Bhattacharya I, Chap 5, pp 25–36, Springer Proceedings in Physics, 166 (Springer India), 2015.
  13. Alfalou A, Situ G, Peng X, He W, Rastogi P, 3DIM-DS 2015: Optical image processing in the context of 3D imaging, metrology, and data security, Opt Lasers Eng, 89(2015)1–202 (Special issue).
  14. Kumar P, Joseph J, Singh K, Double random phase encoding based optical encryption systems using some linear canonical transforms: weaknesses and countermeasures, In: Healy J, Alper Kutay M., Ozaktas H, Sheridan J (eds), Linear Canonical Transforms. Springer Series in Optical Sciences, 198, pp 367–396, (Springer New York), 2016.
  15. Javidi B, Carnicer A, Yamaguchi M, Nomura T, Perez-Cabre E, Millan M S, Nishchal S K, Torroba R, Barrera J F, He W, Peng X, Stern A, Rivenson Y, Al Falou A, Brosseau, C, Guo C, Sheridan J T, Situ, G, Naruse M, Matsumoto T, Juvells I, Lancis J, Chen W, Chen X, Pinkse Prpijn, W H, Mosk A P, Markman A, Roadmap on optical security, J Opt (IOP), 18(2016)1–39.
  16. Singh K, Photorefractive optical cryptography: a personal tour, In Advances in Optical Science and Engineering, Springer Proceedings in Physics194, (Eds) Bhattacharya I, Chakrabarti S, Reehal H S, Lakshminarayanan V, (Springer Nature Singapore Pvt Ltd), 2017.
  17. Alfalou A (ed), Advanced Secure Optical Image Processing for Communications, (IOP Publ, Bristol, U K), 2018.
  18. Nishchal N K, Optical Cryptosystems, (IOP Publishing, Bristol, UK), 2020.
  19. Unnikrishnan G, Singh K, Double random fractional Fourier-domain encoding for optical security, Opt Eng, 39(2000)2853–2859.
  20. Unnikrishnan G, Joseph J, Singh K, Optical encryption by double-random phase encoding in the fractional Fourier domain, Opt Lett, 25 (2000)887–889.
  21. Hennelly B, Sheridan J T, Fractional Fourier trandform-based image encryption: phase retrieval algorithm, Opt Commun, 226(2003)61–80.
  22. Joshi M, Shakher C, Singh K, Color image encryption and decryption using fractional Fourier transform, Opt Commun, 279(2007)35–42.
  23. Lang J, Tao R, Wang Y, Image encryption based on the multiple-parameter discrete fractional Fourier transform and chaos function, Opt Commun, 283(2010)2092–2096.
  24. Maan P, Singh H, Non-linear cryptosystem for image encryption using radial Hilbert mask in fractional Fourier transform domain, 3D Res,9(2018)53; doi.org/10.1007/s13319-018-0205-8.
  25. Girija R, Singh H, A cryptosystem based on deterministic phase masks and fractional Fourier transform deploying singular value decomposition, Opt Quant Electron, 50(2018)210; doi.org/10.1007/s11082-018-1472-6.
  26. Situ G, Zhang J, Double random-phase encoding in the Fresnel domain, Opt Lett, 49 (2004)1584–1586.
  27. Shi Y, Situ G, Zhang J, Multiple image hiding in the Fresnel domain, Opt Lett, 32(2007)1914–1916.
  28. Rajput S K, Nishchal N K, Fresnel domain nonlinear image encryption schems based Gerchberg-Saxton phase retrieval algorithm, Appl Opt, 53(2014)418–425.
  29. Singh H, Yadav A K, Vashisth S, Singh K, Optical image encryption using devil’s vortex toroidal lens in the Fresnel transform domain, Int J Opt, 2015(2015)926135; doi.org/10.1155/2015/926135.
  30. Wang Z, Lv X, Wang H, Hou C, Gong Q, Qin Y, Hierarchical multiple binary image encryption based on a chaos and phase retrieval algorithm in the Fresnel domain, Laser Phys Lett,13(2016)036201; doi.10.1088/1612-2011/13/3/036201.
  31. Singh H, Cryptosystem for securing image encryption using structured phase masks in Fresnel wavelet transform domain, 3D Res, 7(2016); doi.org.10.1007/s13319-016-0110-y.
  32. Zhou N R, Wang Y, Gong L, Novel optical image encryption scheme based on fractional Mellin transform, Opt Commun, 284(2011)3234–3242.
  33. Vashisth S, Singh H, Yadav A K, Singh K, Devil’s vortex phase structure as frequency plane mask for image encryption using the fractional Mellin transform, Int J Opt, 2014(2014)728056; doi.org/10.1155/2014/728056.
  34. Vashisth S, Singh H, Yadav A K, Singh K, Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval, Optik, 125(2014)5309–5315.
  35. Singh H, Watermarking image encryption using deterministic phase mask and singular value decomposition in fractional Mellin transform domain, IET Image Process, 12(2018)1994–2001.
  36. Rodrigo J A, Alieva T, Calvo M L, Gyrator transform: properties and applications, Opt Express, 15(2007)2190–2203.
  37. Singh H, Yadav A K, Vashisth S, Singh K, Fully-phase image encryption using double random-structured phase masks in gyrator domain, Appl Opt, 53(2014)6472–6481.
  38. Singh H, Yadav A K, Vashisth S, Singh K, Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane, Opt Lasers Eng, 67(2015)145–156.
  39. Singh H, Hybrid structured phase mask in frequency plane for optical double image encryption in gyrator transform domain, J Mod Opt, 65(2018)2065–2078.
  40. Khurana M, Singh H, Asymmetric optical image triple masking encryption based on gyrator and Fresnel transforms to remove silhouette problem, 3D Res, (2018); doi.org/10.1007/s13319-018-0190-y.
  41. Khurana M, Singh H, A spiral-phase rear mounted triple masking for secure optical image encryption based on gyrator transform, Recent Patents Comput Sci, 12(2019)80–84.
  42. Singh H, Devil’s vortex Fresnel lens phase masks on an asymmetric cryptosystem based on phase-truncated in gyrator wavelet transform, Opt Lasers Eng, 81(2016)125–139.
  43. Mehra I, Fatima A, Nishchal N K, Gyrator wavelet transform, IET Image Process. 12 (2017)432–437.
  44. Anshula, Singh H, Ensuring security of cryptosystems with DVFM-, modified equal modulus decomposition in the domain of gyrator wavelet transform, Multimed Tools Appl, 82(2022)5965–5985.
  45. Zhao D, Li X, Chen I, Optical image encryption with redefined fractional Hartley transform, Opt Commun, 281(2008) 5326–5329.
  46. Li X, Zhao D, Optical color image encryption with redefined fractional Hartley transform, Optik, 121(2010)673–677.
  47. Singh N, Sinha A, Optical image encryption using improper Hartley transform and chaos, Optik 121(2010)918–925.
  48. Vilardy J M, Torres C O, Jimenez C J, Double image encryption method using the Arnold transform in the fractional Hartley domain, SPIE Proc, 8785(2013)87851R; doi.org/10.1117/12.2022216.
  49. Liu Y, Du J, Fan J, Gong L, Single-channel color image encryption algorithm based on fractional Hartley transform and vector operation, Multimed Tools Appl, 74(2015)3171–3182.
  50. Singh P, Yadav A K, Singh K, Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition, Opt Lasers Eng, 91(2017)187–195.
  51. Yadav A K, Singh P, Singh K, Cryptosystem based on devil’s vortex Fresnel lens in the fractional Hartley domain, J Opt (Springer), 47(2018)208–219.
  52. Yadav A K, Singh P, Saini I, Singh K, Asymmetric encryption algorithm for clour images based on fractional Hartley transform, J Mod Opt, 66(2019)629–642.
  53. Girija R, Singh H. Triple-level cryptosystem using deterministic masks and modified Gerchberg-Saxton iterative algorithm in fractional Hartley domain by positioning singular value decomposition, Optik, 187(2019)238–257.
  54. Singh P, Yadav A K, Vashisth S, Singh K, Review of optical image encryption schemes based on fractional Hartley transform, Asian J Phys, 28(2019)701–716.
  55. Carnicer A, Montes-Usategui M, Arcos S, Juvells I, Vulnerability to chosen-cypher text attacks of optical encryption schemes based on double random phase keys, Opt Lett,30(2005)1644–1646.
  56. Peng X, Chang P, Wei H, Yu B, Known-plaintext attack on optical encryption based on double random phase keys, Opt Lett,31(2006)1044–1046.
  57. Gopinathan G, Monaghan D S, Naughton T J, Sheridan T J. A known plain-text heuristic attack on the Fourier plane encryption algorithm, Opt Express, 14(2006)3181–3186.
  58. Liu W, Yang G, Xie H, A hybrid heuristic algorithm to improve known-plaintext attack on Fourier plane encryption, Opt Express, 17(2009)13928–13938.
  59. Tashima H, Takeda M, Suzuki H, Obi T, Yamaguchi M, Ohyama N, Known-plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack, Opt Express, 18(2010)13772–13781.
  60. Peng X, Wei H, Zhang P, Chosen-plaintext attack on lens-less double-random phase encoding in the Fresnel domain, Opt Lett,31(2006)3261–3263.
  61. Zhang Y, Xiao D, Wen W, Liu H, Vulnerability to chosen-plaintext attack of a general optical encrypytion method with the architecture of scrambling-then-double random phase encoding, Opt Lett, 38(2013)4506–4509.
  62. Qin W, Peng X, Asymmetric cryptosystem based on phase-truncated Fourier transform, Opt Lett, 35 (2010)118–120.
  63. Cai J, Shen X, Lei M, Lin C, Dou S, Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition, Opt Lett,40(2015)475–478.
  64. Abuturab M R, Single-channel color information security system using LU decomposition in gyrator transform domains, Opt Commun, 323(2014)100–109.
  65. Xiong Y, Quan C, Hybrid attack free optical cryptosystem based on two random masks and lower upper decomposition with partial pivoting. Opt Laser Technol, 109(2019)456–464.
  66. Anshula, Singh H, Security enrichment of an asymmetric optical image encryption-based devil’s vortex Fresnel lens phase mask and lower upper decomposition with partial pivoting in gyrator transform domain, Opt Quant Electron, 53(2021)204; doi.org.10.1007/s11082-021-02854-7.
  67. Anjana S, Yadav A K, Singh P, Singh H, Asymmetric double image encryption, compression, and watermarking scheme based on orthogonal-triangular decomposition with column pivoting, Opt Applicata, 52(2022)283–295.
  68. Boukaram, W H, Turkiyyah G, Ltaief H, Keys D E, Batched QR and SCVD algorithms on GPUs with applications in hierarchical matrix compression, Parallel Comput, 74(2018)19–33.
  69. Zhi X, Yan H, Fan J, Zheng X, Efficient discriminative clustering via QR decomposition-based linear analysis, Knowl Based Syst, 153(2018)117–132.
  70. Su Q, Niu Y, Wang G, Jia S, Yue J, Color image blind watermarking scheme based on QR decomposition, Sign Process, 94(2014)219–235.
  71. Abuturab M R, Multiple color-image authentication system using HIS color space and QR decomposition in gyrator domains, J Mod Opt, 63(2016)1035–1050.
  72. Rakheja P, Vig R, Singh P, Double image encryption using 3D Lorenz chaotic system, 2D non-separable linear canonical transform and QR decomposition, Opt Quant Electron, 52(2020)103; doi.org.10.1007/s11082-020-2219-8.
  73. Rakheja P, Singh P, Vig R, An asymmetric image encryption mechanism using QR decomposition in hybrid multi-resolution wavelet domain, Opt Lasers Eng. 134(2020)106177; doi.org/10.1016/j.optlaseng.2020.106177.
  74. Anshula, Singh H, Cryptanalysis for double‑image encryption using the DTLM in frequency plane with QR decomposition and gyrator transform, Opt Rev, 28(2021)596–610.
  75. Anjana S, Yadav A K, Singh P, Singh H, Audio and image encryption scheme based on QR decomposition and random modulus decomposition in Fresnel domain, Opt Applicata, 52(2022)359–374.
  76. Mehra I, Nishchal N K, Fingerprint image encryption using phase retrieval algorithm in gyrator wavelet transform domain using QR decomposition, Opt Commun, 533(2023)129265; doi.org/10.1016/j.optcom.2023.129265.
  77. Golub G, Van Loan C, Matrix computation, (Johns Hopkins Univ Press), 2013.
  78. Strang G, Linear algebra and its applications, 4th edn, (Thomson Learning Inc, USA), 2006.
  79. Barrera J F, Henao R, Torroba R, Optical encryption method using toroidal zone plates, Opt Commun, 248(2005) 35–40.
  80. Barrera J F, Henao R, Torroba R, Fault tolerances using toroidal zone plate encryption, Opt Commun, 256(2005)489–494.
  81. Singh H, Tirth V, Singh R K, Algahtani A,Islam S, Designing of an optical vortices phase mask and used in the frequency domain of linear canonical transform for double image encryption, Imaging Sci J, 68(2022)288–304.
  82. Yadav A K, Vashisth S, Singh H, Singh K, A phase-image watermarking scheme in gyrator domain using devil’s vortex Fresnel lens as a phase mask, Opt Commun, 344 (2015)172–180.
  83. Anshula, Singh H, Optical image encryption using various mathematical transforms and structure phase masks: A review, Asian J Phys, 28 (2020)825–856.
  84. Singh H, Girija, R, Kumar M A, Cryptanalysis of elliptic curve cryptography based on phase truncation in the domain of hybrid gyrator Hartley transform. Opt Quant Electron, 55(2023)487; doi.org.10.1007/s11082-023-04765-1.
  85. Sachin, Singh P, Singh K, Nonlinear image authentication algorithm based on double fractional Mellin domain, Nonlinear Dyn,111(2023)13579–13600.
  86. 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.
  87. Girija R, Singh H., Singh K., An asymmetric cryptosystem using deterministic phase masks, double random phase encoding, orthogonal encoding and decoding, and fractional Fourier transform, Asian J Phys, 32(2023)385–397.
  88. Abuturab M R, Multiple single-channel cryptosystem based on QZdecomposition, CMYK color space fusion and wavelength multiplexing, Opt Quant Electron, 56(2024)365; org.10.1007/s11082–023-06001-2.
  89. Gaur K S, Singh H, Thakran S, Singh K, An asymmetric hybrid cryptosystem based on triple random phase encoding using polar decomposition, QZ modulation, and gyrator domain, Optik,299(2024)171602; org/10.1016/j.ijleo.2023.171602.
  90. Dai J-Y, Zhou N-R, Optical quantum image encryption algorithm with QPSO-BP neural neywork based pseudo random number generator, Quant Inform Process, 22(2023)318; doi.org/10.1007/s11128-023-04071-5.
  91. Gong I, Choi S, Lukin MO, Quantum convolutional neural networks, Nat Phys, 15(2019)1273–1278.
  92. Gong L-H, He X-T, Chang S, Hua T-X, Zhou N-R, Quantum image encryption algorithm based on quantum image XOR operations, Int J Theort Phys, 55(2016)3234–3250.
  93. Fang X, Ren H, Gu M, Orbital angular momentum holography for high-security encryption, Nature Photon, 14 (2020)102–108.
  94. Guo X, Li P, Zhong J, Wen D, Wei B, Liu S, Qi S, Zhao J, Stokes meta-hologram toward optical cryptography, Nat Commun, 13(2022)6687;org/10.1038/s41467-022-34542-9.
  95. Fan Z, Jia Y, Chen H, Qian C, Spatial multiplexing encryption with cascaded metasurfaces, J Opt(IOP), 25(2023)125105; doi.10.1088/2040-8986/ad0659.
  96. Liu S, Wu D, Optical encryption in the photonic orbital angular momentum dimension via direct-laser-writing 3D chiral metahelices, Nano Lett, 23(2023)2304−2311.
  97. Farmani A, Foladi H, Photonic and plasmonic encryption based on reflection-transmission reconfigurable digital coding metasurface in holographic images, J Hogr Appl Phys, 3(2023)63–81.
  98. Zhang F, Guo Y, Pu M, Chen L, Xu M, Liao M, Li L, Li X, Ma X, Luo X, Meta-optics empowered vector visual cryptography for high security and rapid decryption, Nature Commun, 14(2023)1946; doi.org/10.1038/s41467-023-37510-z.
  99. Zhou Q, Wang X, Jin M, Zhang L, Xu B, Optical image encryption based on two-channel detection and deep learning, Opt Lasers Eng,162(2023)107415; doi.org/10.1016/j.optlaseng.2022.10741.
  100. Zhuang X, Yan A, Deep-learning based cipher-text only attack on optical scanning cryptosystem, Opt Laser Technol, 157(2023)108744; doi.org/10.1016/j.optlastec.2022.108744.
  101. Xue J-d, Wang X-g, Zhou Q-m, Zhang L, Yao M, Deep-learning-assisted optical steganographic encryption via ghost encoding and binary hologram, Opt Lasers Eng, 172(2024); doi.org/10.1016/j.optlaseng.2023.107891.
A secure image encryption method using toroidal vortex phase masks, QR decomposition, and gyrator transformDownload

Related Posts