## Space-based optical image encryption |

Optics Express, Vol. 18, Issue 26, pp. 27095-27104 (2010)

http://dx.doi.org/10.1364/OE.18.027095

Acrobat PDF (1291 KB)

### Abstract

In this paper, we propose a new method based on a three-dimensional (3D) space-based strategy for the optical image encryption. The two-dimensional (2D) processing of a plaintext in the conventional optical encryption methods is extended to a 3D space-based processing. Each pixel of the plaintext is considered as one particle in the proposed space-based optical image encryption, and the diffraction of all particles forms an object wave in the phase-shifting digital holography. The effectiveness and advantages of the proposed method are demonstrated by numerical results. The proposed method can provide a new optical encryption strategy instead of the conventional 2D processing, and may open up a new research perspective for the optical image encryption.

© 2010 OSA

## 1. Introduction

## 2. Theoretical analysis

*z*and

*λ*denotes the wavelength of a light source, wave number

*ρ*is the distance from the particle in the object plane to a point in the phase-only mask (M2) plane

24. W. Chen and X. Chen, “Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain,” Opt. Express **18**(13), 13536–13541 (2010). [CrossRef] [PubMed]

25. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. **22**(16), 1268–1270 (1997). [CrossRef] [PubMed]

26. I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting digital holography,” Appl. Opt. **45**(5), 975–983 (2006). [CrossRef] [PubMed]

*ℑ*denotes an incorporating operation. Each pixel of the plaintext is extracted based on a back-propagation algorithm using a specific distance, and the decrypted image

## 3. Results and discussion

14. A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. **30**(13), 1644–1646 (2005). [CrossRef] [PubMed]

16. X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. **31**(22), 3261–3263 (2006). [CrossRef] [PubMed]

1. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. **20**(7), 767–769 (1995). [CrossRef] [PubMed]

5. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. **29**(14), 1584–1586 (2004). [CrossRef] [PubMed]

8. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. **25**(12), 887–889 (2000). [CrossRef]

14. A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. **30**(13), 1644–1646 (2005). [CrossRef] [PubMed]

16. X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. **31**(22), 3261–3263 (2006). [CrossRef] [PubMed]

14. A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. **30**(13), 1644–1646 (2005). [CrossRef] [PubMed]

16. X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. **31**(22), 3261–3263 (2006). [CrossRef] [PubMed]

## 4. Conclusions

## Acknowledgements

## References and links

1. | P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. |

2. | B. Javidi, “Securing information with optical technologies,” Phys. Today |

3. | O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE |

4. | O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. |

5. | G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. |

6. | N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. |

7. | Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. |

8. | G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. |

9. | H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, |

10. | X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express |

11. | H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Express |

12. | M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express |

13. | Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express |

14. | A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. |

15. | X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. |

16. | X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. |

17. | T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A |

18. | X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. |

19. | P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. |

20. | W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. |

21. | J. W. Goodman, |

22. | U. Schnars, and W. Jueptner, |

23. | W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. |

24. | W. Chen and X. Chen, “Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain,” Opt. Express |

25. | I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. |

26. | I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting digital holography,” Appl. Opt. |

27. | B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. |

28. | F. J. Dyson and H. Falk, “Period of a discrete cat mapping,” Am. Math. Mon. |

29. | W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. |

30. | Y. Sheng, Z. Xin, M. S. Alam, L. Xi, and L. Xiao-Feng, “Information hiding based on double random-phase encoding and public-key cryptography,” Opt. Express |

31. | X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. |

32. | C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. |

33. | M. Antkowiak, N. Callens, C. Yourassowsky, and F. Dubois, “Extended focused imaging of a microparticle field with digital holographic microscopy,” Opt. Lett. |

**OCIS Codes**

(100.2000) Image processing : Digital image processing

(100.6890) Image processing : Three-dimensional image processing

(090.1995) Holography : Digital holography

(100.4998) Image processing : Pattern recognition, optical security and encryption

**ToC Category:**

Image Processing

**History**

Original Manuscript: October 20, 2010

Revised Manuscript: December 5, 2010

Manuscript Accepted: December 6, 2010

Published: December 8, 2010

**Citation**

Wen Chen and Xudong Chen, "Space-based optical image encryption," Opt. Express **18**, 27095-27104 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-26-27095

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### References

- P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995). [CrossRef] [PubMed]
- B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997). [CrossRef]
- O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009). [CrossRef]
- O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999). [CrossRef]
- G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004). [CrossRef] [PubMed]
- N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009). [CrossRef]
- Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12(3), 035407 (2010). [CrossRef]
- G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000). [CrossRef]
- H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform With Applications in Optics and Signal Processing (Wiley, Singapore, 2001).
- X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10(1), 41–45 (2002). [PubMed]
- H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Express 12(20), 4912–4921 (2004). [CrossRef] [PubMed]
- M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17(25), 22462–22473 (2009). [CrossRef]
- Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18(11), 12033–12043 (2010). [CrossRef] [PubMed]
- A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30(13), 1644–1646 (2005). [CrossRef] [PubMed]
- X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006). [CrossRef] [PubMed]
- X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31(22), 3261–3263 (2006). [CrossRef] [PubMed]
- T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25(10), 2608–2617 (2008). [CrossRef]
- X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, “Security enhancement of double-random phase encryption by amplitude modulation,” Opt. Lett. 33(14), 1575–1577 (2008). [CrossRef] [PubMed]
- P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. 34(3), 331–333 (2009). [CrossRef] [PubMed]
- W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010). [CrossRef] [PubMed]
- J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
- U. Schnars, and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, New York, 2005).
- W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95(20), 201103 (2009). [CrossRef]
- W. Chen and X. Chen, “Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain,” Opt. Express 18(13), 13536–13541 (2010). [CrossRef] [PubMed]
- I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997). [CrossRef] [PubMed]
- I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting digital holography,” Appl. Opt. 45(5), 975–983 (2006). [CrossRef] [PubMed]
- B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28(4), 269–271 (2003). [CrossRef] [PubMed]
- F. J. Dyson and H. Falk, “Period of a discrete cat mapping,” Am. Math. Mon. 99(7), 603–614 (1992). [CrossRef]
- W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282(18), 3680–3685 (2009). [CrossRef]
- Y. Sheng, Z. Xin, M. S. Alam, L. Xi, and L. Xiao-Feng, “Information hiding based on double random-phase encoding and public-key cryptography,” Opt. Express 17(5), 3270–3284 (2009). [CrossRef] [PubMed]
- X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. 11(8), 085402 (2009). [CrossRef]
- C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47(19), D71–D79 (2008). [CrossRef] [PubMed]
- M. Antkowiak, N. Callens, C. Yourassowsky, and F. Dubois, “Extended focused imaging of a microparticle field with digital holographic microscopy,” Opt. Lett. 33(14), 1626–1628 (2008). [CrossRef] [PubMed]

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