Asian Journal of Physics Vol. 34, Nos 7 & 8 (2025) 557-568

Dual-user asymmetric medical signal encryption algorithm in multi-domain system

Poonam Kumari1, Himani2 and Sachin1
1Department of Mathematics, IIHS, Kurukshetra University, Kurukshetra-136 119, Haryana, India,
2Department of Mathematics, Kurukshetra University, Kurukshetra-136 119, Haryana, India,

Dedicated to Prof Kehar Singh on the occasion of his 84th Birth Day on July 3, 2025


This manuscript proposes a dual-user encryption algorithm in the Fresnel and Fourier domain using polar decomposition (PD). The algorithm’s asymmetric nature provides an additional level of protection to the proposed algorithm. The algorithm is tested with the medical image. The efficacy and sturdiness of the proposed method are measured through various statistical and visual attacks like information entropy, mean squared error, peak signal noise ratio, correlation coefficient, histogram, mesh, and correlation distribution plots. The results assess the robustness and effectiveness of the proposed scheme against cryptographic attacks. The results substantiate that the proposed algorithm is safe and secure. © Anita Publications. All rights reserved.
Doi: 
Keywords: Fresnel Transform, Fourier Transform, Image Encryption, Polar Decomposition, Asymmetric Encryption


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

  1. Biryukov A, The boomerang attack on 5 and 6-round reduced AES, in Advanced Encryption Standard – AES, vol. 3373, Hutchison D, Kanade T, Kittler J, Kleinberg J M, Mattern F, Mitchellm J C, Naor M, Nierstrasz O, Rangan C P, Steffen B, Sudan M, Terzopoulos D, Tygar D, Vardi M Y, Weikum G, Dobbertin H, Rijmen V, Sowa A, (eds), (Berlin, Heidelberg: Springer Berlin Heidelberg), 2005, pp 11–15; doi. 10.1007/11506447_2.
  2. Hasib A A, Haque AAMM, A comparative study of the performance and security issues of AES and RSA cryptography, in 2008 Third International Conference on Convergence and Hybrid Information Technology, Busan, Korea, pp 505–510; doi.10.1109/ICCIT.2008.179.
  3. Javidi B, Fault tolerance properties of a double phase encoding encryption technique, Opt Eng, 36(1997)992; doi. 10.1117/1.601144.
  4. Kishk S, Javidi B, Information hiding technique with double phase encoding, Appl Opt, 41(2002)5462; doi. 10.1364/AO.41.005462.
  5. Wang Y, Quan C, Tay C J, Optical color image encryption without information disclosure using phase-truncated Fresnel transform and a random amplitude mask, Opt Commun, 344(2015)147–155.
  6. Xu H, Xu W, Wang S, Wu S, Asymmetric optical cryptosystem based on modulus decomposition in Fresnel domain, Opt Commun, 402(2017)302–310.
  7. 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; doi: 10.1364/AO.53.006472.
  8. 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.
  9. Kumar J, Singh P, Yadav A K, Kumar A, Asymmetric cryptosystem for phase images in fractional Fourier domain using LU-decomposition and Arnold transform, Procedia Comput Sci, 132(2018)1570–1577.
  10. Chen H, Du X, Liu Z, Optical spectrum encryption in associated fractional Fourier transform and gyrator transform domain, Opt Quant Electron, 48(2015)12; doi.10.1007/s11082-015-0291-2.
  11. Xiong Y, Kumar R, Quan C, Security analysis on an optical encryption and authentication scheme based on phase-truncation and phase-retrieval algorithm, IEEE Photonics J, 11(2019)1–14; doi: 10.1109/JPHOT.2019.2936236.
  12. Unnikrishnan G, Joseph J, Singh K, Optical encryption by double-random phase encoding in the fractional Fourier domain, Opt Lett, 25(2000)887; doi.10.1364/OL.25.000887.
  13. Midoun M A, Wang X, Talhaoui M Z, A sensitive dynamic mutual encryption system based on a new 1D chaotic map, Opt Lasers Eng, 139(2021)106485; doi: 10.1016/j.optlaseng.2020.106485.
  14. 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; doi. 10.1364/OL.31.001044.
  15. 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; doi.10.1364/OE.18.013772.
  16. Chen W, Javidi B, Chen X, Advances in optical security systems, Adv Opt Photon, 6(2914)120; doi.10.1364/AOP.6.000120.
  17. Ahouzi E, Zamrani W, Azami N, Lizana A, Campos J, Yzuel M J, Optical triple random-phase encryption, Opt Eng, 56(2017)113114; doi.10.1117/1.OE.56.11.113114.
  18. Kumar R, Quan C, Optical colour image encryption using spiral phase transform and chaotic pixel scrambling, J Mod Opt, 66(2019)776–785.
  19. Anjana S, Saini I, Singh P, Yadav A K, Asymmetric cryptosystem using affine transform in Fourier domain, in Advanced Computational and Communication Paradigms, vol 706, Bhattacharyya S, Chaki N, Konar D, Chakraborty U K, Singh C T, (Eds), (Singapore: Springer Singapore), 2018, pp 29–37; doi: 10.1007/978-981-10-8237-5_4.
  20. Frauel Y, Castro A, Naughton T J, Javidi B, Security analysis of optical encryption, Carapezza E M (Ed), (Bruges, Belgium), Oct 2005, p 598603; doi. 10.1117/12.633677.
  21. Wang X, Chen Y, Dai C, Zhao D, Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform, Appl Opt, 53(2014)208; doi. 10.1364/AO.53.000208.
  22. Wang X, Zhao D, A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms, Opt Commun, 285(2012)1078–1081.
  23. 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; doi. 10.1364/OL.40.000475.
  24. Deng X, Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition: comment, Opt Lett, 40(2015)3913; doi.10.1364/OL.40.003913.
  25. Rakheja P, Vig R, Singh P, An asymmetric watermarking scheme based on random decomposition in hybrid multi-resolution wavelet domain using 3D Lorenz chaotic system, Optik, 198(2019)163289; doi: 10.1016/j.ijleo.2019.163289.
  26. 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: 10.1016/j.optlaseng.2020.106399.
  27. Sachin, Kumar R, Singh P, Multiuser optical image authentication platform based on sparse constraint and polar decomposition in Fresnel domain, Phys Scr, 97(2022)115101; doi. 10.1088/1402-4896/ac925d.
  28. Peng X, Wei H, Zhang P, Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain, Opt Lett, 31(2006)3261; doi. 10.1364/OL.31.003261.
  29. Goodman J W, Introduction to Fourier Optics, 3rd edn, vol 1, (Roberts & Co. Publishers), 2005.
  30. Refregier P, Javidi B, Optical image encryption based on input plane and Fourier plane random encoding, Opt Lett, 20(1995)767; doi: 10.1364/OL.20.000767.
  31. Sachin, Kumar R, Sakshi, Yadav R, Reddy S G, Yadav A K, Singh P, Advances in Optical Visual Information Security: A Comprehensive Review, Photonics, 11(2024)99; doi: 10.3390/photonics11010099.
  32. Kumar R, Zhong F, Quan C, Optical voice information hiding using enhanced iterative algorithm and computational ghost imaging, J Opt, 21(2019)065704; doi: 10.1088/2040-8986/ab1e32.
  33. Sachin Kumar R, Singh P, New modified plaintext-attacks in a session for optical cryptosystem based on DRPE with PFS, Appl Opt, 61(2021)623–628.
  34. Yadav R, Singh P, Asymmetric image authentication algorithm using double random modulus decomposition and CGI, Comp Appl Math, 42(2023)305; doi.10.1007/s40314-023-02443-2.
  35. Girija R, Singh H, A robust correlation analysis framework for imbalanced and dichotomous data with uncertainty,” 3D Res, 9(2018)42; doi.10.1007/s13319-018-0192-9.
  36. Monaghan D S, Gopinathan U, Naughton T J, Sheridan J T, A numerical analysis of double random phase encryption, Optical Information Systems IV, SPIE, Aug. 2006, pp. 222–230; doi.10.1117/12.680744.
  37. Cai Z, Chen J, Pedrini G, Osten W, Liu X, Peng X, Lensless light-field imaging through diffuser encoding, Light Sci Appl, 9(2020)143; doi.10.1038/s41377-020-00380-x.
  38. Lopez-Caloca A, Escalante-Ramirez B, The Hermite transform: An efficient tool for noise reduction and image fusion in remote-sensing, in Image Processing for Remote Sensing, Chen C (ed), (CRC Press), 2007, pp 273–291; doi.10.1201/9781420066654.ch12.
  39. Gopinathan G, Monaghan D S, Naughton T J, Sheridan J T, A known-plaintext heuristic attack on the Fourier plane encryption algorithm, Opt Express, 14(2006)3181–3186.
  40. Li T, Shi Y, Vulnerability of impulse attack-free four random phase mask cryptosystems to chosen-plaintext attack,” J Opt, 18(2016)035702; doi: 10.1088/2040-8978/18/3/035702.
  41. 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.
  42. Qin W, Peng X, Meng X, He W, Improved Known-Plaintext Attack on Optical Encryption Based on Double Random Phase Encoding, in 2010 Symposium on Photonics and Optoelectronics, Jun. 2010, pp. 1–4; doi: 10.1109/SOPO.2010.5504346.