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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 33 — Nov. 20, 2006
  • pp: 8434–8439

Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform

Zhou Xin, Yuan Sheng, Sheng-wei Wang, and Xie Jian  »View Author Affiliations

Applied Optics, Vol. 45, Issue 33, pp. 8434-8439 (2006)

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An affine mapping mathematical expression of the double-random-phase encryption technique has been deduced utilizing the matrix form of discrete fractional Fourier transforms. This expression clearly describes the encryption laws of the double-random-phase encoding techniques based on both the fractional Fourier transform and the ordinary Fourier transform. The encryption process may be regarded as a substantial optical realization of the affine cryptosystem. It has been illustrated that the encryption process converts the original image into a white Gaussian noise with a zero-mean value. Also, the decryption process converts the data deviations of the encrypted image into white Gaussian noises, regardless of the type of data deviations. These noises superimpose on the decrypted image and degrade the signal-to-noise ratio. Numerical simulations have been implemented for the different types of noises introduced into the encrypted image, such as the white noise with uniform distribution probability, the white noise with Gaussian distribution probability, colored noise, and the partial occlusion of the encrypted image.

© 2006 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.4560) Fourier optics and signal processing : Data processing by optical means
(070.6020) Fourier optics and signal processing : Continuous optical signal processing

Original Manuscript: May 10, 2006
Revised Manuscript: July 31, 2006
Manuscript Accepted: August 5, 2006

Zhou Xin, Yuan Sheng, Wang Sheng-wei, and Xie Jian, "Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform," Appl. Opt. 45, 8434-8439 (2006)

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  1. P. Refregier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769 (1995). [CrossRef] [PubMed]
  2. S. Kishk and B. Javidi, "Information hiding technique with double phase encoding," Appl. Opt. 41, 5462-5470 (2002). [CrossRef] [PubMed]
  3. R. Wang and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. 35, 2464-2469 (1996). [CrossRef]
  4. O. Matoba and B. Javidi, "Secure holographic memory by double-random polarization encryption," Appl. Opt. 43, 2915-2919 (2004). [CrossRef] [PubMed]
  5. F. Goudail, F. Bollaro, B. Javidi, and P. Refregier, "Influence of a perturbation in a double phase-encoding system," J. Opt. Soc. Am. A 15, 2629-2638 (1998). [CrossRef]
  6. B. Wang and C.-C. Sun, "Enhancement of signal-to-noise ratio of a double random phase encoding encryption system," Opt. Eng. 40, 1502-1505 (2001). [CrossRef]
  7. S. Liu, L. Yu, and B. Zhu, "Optical image encryption by cascaded fractional Fourier transforms with random phase filtering," Opt. Commun. 187, 57-63 (2001). [CrossRef]
  8. G. Unnikrishnan and K. Singh, "Optical encryption using quadratic phase systems," Opt. Commun. 193, 51-67 (2001). [CrossRef]
  9. N. K. Nishchal, J. Joseph, and K. Singh, "Securing information using fractional Fourier transforms in digital holography," Opt. Commun. 235, 253-259 (2004). [CrossRef]
  10. R. Qiwen, Wavelet Transform and Fractional Fourier Transform Theory and Applications (HaErbin U. Press, 2001) (in Chinese).
  11. C. C. Shih, "Fractionalization of Fourier transform," Opt. Commun. 48, 495-498 (1995). [CrossRef]
  12. C. Candan, M. A. Kutay, and H. M. Ozaktas, "The discrete fractional Fourier transformation," IEEE Trans. Signal Process. 48, 1329-1337 (2000). [CrossRef]
  13. D. R. Stinson, Cryptography: Theory and Practice, 2nd ed. (CRC Press, 2002).
  14. L. Yuanlie, Applied Stochastic Process (Qinghua U. Press, 2003) (in Chinese).
  15. S. M. Ross, Stochastic Processes (Wiley, 1983).

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