Current Optics and Photonics

Optical Society of Korea (한국광학회)
권호 표지
DOI QR코드

DOI QR Code

Avalanche and Bit Independence Properties of Photon-counting Double Random Phase Encoding in Gyrator Domain

  • Lee, Jieun (Division of IT Convergence Engineering, Hansung University) ;
  • Sultana, Nishat (Department of Computer Engineering, Chosun University) ;
  • Yi, Faliu (Department of Clinical Science, University of Texas Southwestern Medical Center) ;
  • Moon, Inkyu (Department of Robotics Engineering, DGIST)
  • Received : 2018.05.01
  • Accepted : 2018.07.04
  • Published : 2018.08.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we evaluate cryptographic properties of a double random phase encoding (DRPE) scheme in the discrete Gyrator domain with avalanche and bit independence criterions. DRPE in the discrete Gyrator domain is reported to have higher security than traditional DRPE in the Fourier domain because the rotation angle involved in the Gyrator transform is viewed as additional secret keys. However, our numerical experimental results demonstrate that the DRPE in the discrete Gyrator domain has an excellent bit independence feature but does not possess a good avalanche effect property and hence needs to be improved to satisfy with acceptable avalanche effect that would be robust against statistical-based cryptanalysis. We compare our results with the avalanche and bit independence criterion (BIC) performances of the conventional DRPE scheme, and improve the avalanche effect of DRPE in the discrete Gyrator domain by integrating a photon counting imaging technique. Although the Gyrator transform-based image cryptosystem has been studied, to the best of our knowledge, this is the first report on a cryptographic evaluation of discrete Gyrator transform with avalanche and bit independence criterions.

Keywords

References

  1. H. Farid, "Image forgery detection," IEEE Signal Process. Mag. 26, 16-25 (2009). https://doi.org/10.1109/MSP.2008.931079
  2. M. Stamp, Information Security: Principles and Practice (Wiley, 2011).
  3. S. Kishk and B. Javidi, "3D object watermarking by a 3D hidden object," Opt. Express 11, 874-888 (2003) https://doi.org/10.1364/OE.11.000874
  4. Y. Sheng, Z. Xin, M. Alam, L. Xin, and L. Xiao-Feng, "Information hiding based on double random-phase encoding and public-key cryptography," Opt. Express 17, 3270-3284 (2009). https://doi.org/10.1364/OE.17.003270
  5. F. Yi, I. Moon, and Y. Lee, "A multispectral photon-counting double random phase encoding scheme for image authentication," Sensors 14, 8877-8894 (2014). https://doi.org/10.3390/s140508877
  6. H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, "Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane," Opt. Lasers Eng. 67, 145-156 (2015). https://doi.org/10.1016/j.optlaseng.2014.10.011
  7. T. Zhao, Q. Ran, L. Yuan, Y. Chi, and J. Ma, "Information verification cryptosystem using one-time keys based on double random phase encoding and public-key cryptography," Opt. Lasers Eng. 83, 48-58 (2016). https://doi.org/10.1016/j.optlaseng.2016.03.001
  8. X. Wang, W. Chen, and X. Chen, "Optical information authentication using compressed double-random-phase-encoded images and quick-response codes," Opt. Express 23, 6239-6253 (2015). https://doi.org/10.1364/OE.23.006239
  9. P. Réfrégier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769 (1995). https://doi.org/10.1364/OL.20.000767
  10. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett. 29, 1584-1586 (2004). https://doi.org/10.1364/OL.29.001584
  11. N. Singh and A. Sinha, "Gyrator transform-based optical image encryption, using chaos," Opt. Lasers Eng. 47, 539-546 (2009). https://doi.org/10.1016/j.optlaseng.2008.10.013
  12. I. Moon, F. Yi, Y. H. Lee, and B. Javidi, "Avalanche and bit independence characteristics of double random phase encoding in the fourier and fresnel domains," J. Opt. Soc. Am. A 31, 1104-1111 (2014). https://doi.org/10.1364/JOSAA.31.001104
  13. Z. Liu, X. Lie, C. Lin, J. Dai, and S. Liu, "Image encryption scheme by using iterative random phase encoding in gyrator transform domains," Opt. Lasers Eng. 49, 542-546 (2011). https://doi.org/10.1016/j.optlaseng.2010.12.005
  14. S. Daza, F. Vega, L. Matos, C. Moreno, M. Diaz, and Y. Daza, "Image encryption based on convolution operation in the gyrator transform domain," in Proc. IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society (Canada, Oct. 2012), pp. 1527-1529.
  15. Z. Liu, Y. Zhang, S. Li, W. Liu, W. Liu, Y. Wang, and S. Liu, "Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains," Opt. Lasers Technol. 47, 152-158 (2013). https://doi.org/10.1016/j.optlastec.2012.09.007
  16. Q. Wang, Q. Guo, and L. Lei, "Multiple-image encryption system using cascaded phase mask encoding and a modified Gerchberg-Saxton algorithm in gyrator domain," Opt. Commun. 320, 12-21 (2012).
  17. M. Abuturab, "Color image security system using double random-structured phase encoding in gyrator transform domain," Appl. Opt. 51, 3006-3016 (2012). https://doi.org/10.1364/AO.51.003006
  18. M. Abuturab, "An asymmetric color image cryptosystem based on Schur decomposition in gyrator transform domain," Opt. Lasers Eng. 58, 39-47 (2014).
  19. J. Sang, J. Zhao, Z. Xiang, B. Cai, and H. Xiang, "Security analysis of image encryption based on gyrator transform by searching the rotation angle with improved PSO algorithm," Sensors 15, 19199-19211 (2015). https://doi.org/10.3390/s150819199
  20. Z. Liu, D. Chen, J. Ma, S. Wei, Y. Zhang, J. Dai, and S. Liu, "Fast algorithm of discrete gyrator transform based on convolution operation," Optik - Int. J. Light Electron Opt. 122, 864-867 (2011). https://doi.org/10.1016/j.ijleo.2010.06.010
  21. J. Chen, Z. Zhu, C. Fu, L. Zhang, and H. Yu, "Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains," Opt. Lasers Eng. 66, 1-9 (2015).
  22. E. Pérez-Cabré, C. Héctor, S María, and B. Javidi, "Photon-counting double-random-phase encoding for secure image verification and retrieval," J. Opt. 14, 094001 (2012). https://doi.org/10.1088/2040-8978/14/9/094001
  23. E. Perez-Cabre, M. Cho, and B. Javidi, "Information authentication using photon-counting double-random-phase encrypted images," Opt. Lett. 36, 22-24 (2010).
  24. Z. Xin, D. Lai, S. Yuan, D. Li, and J. Hu, "A method for hiding information utilizing double-random phase-encoding technique," Opt. Lasers Technol. 39, 1360-1363 (2007). https://doi.org/10.1016/j.optlastec.2006.11.002
  25. G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett. 25, 887-889 (2000). https://doi.org/10.1364/OL.25.000887
  26. G. Li, W. Yang, D. Li, and G. Situ, "Cyphertext-only attack on the double random-phase encryption: Experimental demonstration," Opt. Express 25, 8690-8697 (2017). https://doi.org/10.1364/OE.25.008690
  27. X. Liu, J. Wu, W. He, M. Liao, C. Zhang, and X. Peng, "Vulnerability to ciphertext-only attack of optical encryption scheme based on double random phase encoding," Opt. Express 23, 18955-18968 (2015). https://doi.org/10.1364/OE.23.018955
  28. T. Li and Y. Shi, "Attack on optical double random phase encryption based on the principle of ptychographical imaging," Chin. Phys. Lett. 33, 014206 (2016). https://doi.org/10.1088/0256-307X/33/1/014206
  29. H. Li, "Image encryption based on gyrator transform and two-step phase-shifting interferometry," Opt. Lasers Eng. 47, 45-50 (2009). https://doi.org/10.1016/j.optlaseng.2008.08.001
  30. J. Rodrigo, A. Tatiana, and L. Maria, "gyrator transform: properties and applications," Opt. Express 15, 2190-2203 (2007). https://doi.org/10.1364/OE.15.002190
  31. M. Juan, O. Vilardy, S. Maria, and E. Perez-Cabre, "Secure image encryption and authentication using the photon counting technique in the Gyrator domain," in Proc. 20th Symposium on Signal Processing, Images and Computer Vision (STSIVA)(Colombia, Sept. 2015), pp. 1-6.
  32. S. Rajput, D. Kumar, and N. Nishchal, "Photon counting imaging and phase mask multiplexing for multiple images authentication and digital hologram security," Appl. Opt. 54, 1657-1666 (2015). https://doi.org/10.1364/AO.54.001657
  33. H. Feistel, "Cryptography and computer privacy," Sci. Am. 228, 15-23 (1973).
  34. S. Gupta and S. Yadav, "Performance analysis of cryptographic hash functions," Int. J. Sci. Res. 4, 2319-7064 (2015).
  35. C. Blondeau and K. Nyberg, "New links between differential and linear cryptanalysis," Lect. Notes Comput. Sci. 7881, 388-404 (2013).
  36. V. Goyal, A. O'Neill, and V. Rao, Correlated-input secure hash functions (Springer, 2011).
  37. W. Stallings, Cryptography and Network Security Principles and Practice (Prentice Hall, 2011).
  38. J. Castro, J. Sierra, A. Seznec, A. Izquierdo, and A. Ribagorda, "The strict avalanche criterion randomness test," Math. Comput. Simul. 68, 1-7 (2005). https://doi.org/10.1016/j.matcom.2004.09.001
  39. A. ALabaichi, R. Mahmod, and F. Ahmad, "Analysis of some security criteria for S-boxes in blowfish algorithm," Int. J. Digit. Content Technol. Appl. 7, 8-20 (2013). https://doi.org/10.4156/jdcta.vol7.issue3.2