Asian Journal of Physics Vol. 30 Nos 8 & 9 (2021) 1397-1406

Security-analysis of a nonlinear mask-based cryptosystem in fractional Mellin domain

Phool Singh1, A K Yadav2 and Kehar Singh3


This paper presents security-analysis of a fractional Mellin transform based cryptosystem that uses a non-linear mask in the spatial domain. An input image is bonded with a random phase mask and then a spatially separated nonlinear mask is added to it. Thereafter, fractional Mellin transform operation is carried out to get the encrypted image. An inverse fractional Mellin transform is performed on the encrypted image to recover the original image. The scheme is validated for grayscale images of size 256×256 pixels. Security analysis of the scheme is carried out in terms of the statistical attack, contamination attack, occlusion attack, and special known-plaintext attack. It is found that the scheme resists the statistical attacks, contamination attack, and occlusion attack, but is vulnerable to the special known-plaintext attack. © Anita Publications. All rights reserved.
Keywords: Nonlinear mask, Fractional Mellin transform, Grayscale images, Security analysis.

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


  1. Nishchal N K, Optical Cryptosystems, (IOP Publishing, Bristol U K) 2019.
  2. Refregier P, Javidi B, Optical image encryption based on input plane and Fourier plane random encoding, Opt Lett, 20(1995)767–769.
  3. Unnikrishnan G, Singh K, Double random fractional Fourier-domain encoding for optical security, Opt Eng, 39 (2000)2853;
  4. Singh P, Yadav A K, Singh K, Saini I, Optical image encryption in the fractional Hartley domain, using Arnold transform and singular value decomposition, AIP Conf Proc, 1802(2017)020017-1-7; org/10.1063/1.4973267.
  5. Kumar J, Singh P, Yadav A K, Asymmetric cryptosystem using double random-decomposition in fractional Fourier transform domain, Proc SPIE, 10751(2018)107510V; org/10.1117/12.2321973.
  6. Chen H, Du X, Liu Z, Optical spectrum encryption in associated fractional Fourier transform and gyrator transform domain, Opt Quant Electron, 48(2015)1–12.
  7. Kumari E, Mukherjee S, Singh P, Kumar R, Asymmetric color image encryption and compression based on discrete cosine transform in Fresnel domain, Results in Opt, 1(2020)100005-100014;org/10.1016/
  8. Agoyi M, Celebi E, Anbarjafari G, A watermarking algorithm based on chirp z-transform, discrete wavelet transform, and singular value decomposition, Signal Image Video Process, 9(2015)735–745.
  9. Zhou N, Wang Y, Gong L, Novel optical image encryption scheme based on fractional Mellin transform, Opt Commun, 284(2011)3234–3242.
  10. Rakheja P, Vig R, Singh P, Singh R, An iris biometric protection scheme using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain, Opt Quant Electron, 51(2019)204–223.
  11. Mehra I, Nishchal N K, Imge fusion using wavelet transform and its application to asymmetric cryptosystem and hiding, Opt Express, 22(2014)5474–5482.
  12. Mehra I, Nishchal N K, Optical asymmetric image encryption using gyrator wavelet transform, Opt Commun, 354 (2015)344–352.
  13. Singh P, Yadav A K, Singh K, Saini I, Asymmetric watermarking scheme in fractional Hartley domain using modified equal modulus decomposition. J Optoelectron Adv Mater, 21(2019)484–491.
  14. Yadav A K, Singh P, Singh K, Cryptosystem based on devil’s vortex Fresnel lens in the fractional Hartley domain. J Opt, 47( 2018)208–219.
  15. Zhou N, Wang Y, Gong L, Chen X, Yang Y, Novel color image encryption algorithm based on the reality preserving fractional Mellin transform, Opt Laser Technol, 44(2012)2270–2281.
  16. Zhou N, Liu X, Zhang Y, and Yang Y, Image encryption scheme based on fractional Mellin transform and phase retrieval technique in fractional Fourier domain, Opt Laser Technol, 47(2013)341–346.
  17. 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.
  18. Nakano k, Takeda M, Suzuki H, Yamaguchi M, security analysis of phase-only DRPE based on known-plaintext attack using multiple known plaintext–ciphertext pairs, Opt Lett, 53(2014)6435-6444.
  19. 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.
  20. 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.
  21. Qin W, Vulnerability to chosen-plaintext attack of optoelectronic information encryption with phase-shifting interferometry, Opt Eng, 50(2011)065601;
  22. Javidi B, Carnicer A, Yamaguchi M, Nomura T, Pérez-Cabré E, Millán A S, Nishchal N K, Torroba R, Barrera, J F, He W, Peng X, Stern A, Rivenson Y, Alfalou A, Brosseau C, Guo C, Sheridan J T, Situ G, Naruse M, Matsumoto T, Juvells I, Tajahuerce E, Lancis J, Chen W, Chen X, Pinkse, P W H, Mosk A P, Markman A, Roadmap on optical security, J Opt (IOP), 18(2016)083001;
  23. Dou S, Shen X, Lin C. Security-enhanced optical nonlinear cryptosystem based on double random phase encoding. Opt Laser Technol, 123(2020)105897;
  24. Singh P, Kumar R, Yadav A K, Singh K, Security analysis and modified attack algorithms for a nonlinear optical cryptosystem based on DRPE, Opt Lasers Eng,139(2021)106501;
  25. Wang M, Pousset Y, Carre P, Perrine C, Zhou N, Wu J, Optical image encryption scheme based on apertured fractional Mellin transform, Opt Laser Technol, 124(2020)106001;
  26. Wang M, Pousset Y, Carre p, Perrine C, Zhou N, Wu J, Image encryption scheme based on a Gaussian apertured reality-preserving fractional Mellin transform, Opt Appl, 3(2020)477–495.
  27. Wang M, Li L, Duan H, Xu M, Optical double-image encryption based on Gaussian apertured reality-preserving fractional Mellin transform, J Mod Opt, 68(2021) 753–770.
  28. Abuturab M R, Securing multiple-single-channel color image using unequal spectrum decomposition and 2D-SLIM biometric keys, Opt Commun, 493(2021)127034;
  29. Barfungpa S P, Abuturab M R, Asymmetric cryptosystem using coherent superposition and equal modulus decomposition of fractional Fourier spectrum, Opt Quant Electron, 48(2016)520–535.