## Double images encryption method with resistance against the specific attack based on an asymmetric algorithm |

Optics Express, Vol. 20, Issue 11, pp. 11994-12003 (2012)

http://dx.doi.org/10.1364/OE.20.011994

Acrobat PDF (1283 KB)

### Abstract

A double-image encryption technique that based on an asymmetric algorithm is proposed. In this method, the encryption process is different from the decryption and the encrypting keys are also different from the decrypting keys. In the nonlinear encryption process, the images are encoded into an amplitude cyphertext, and two phase-only masks (POMs) generated based on phase truncation are kept as keys for decryption. By using the classical double random phase encoding (DRPE) system, the primary images can be collected by an intensity detector that located at the output plane. Three random POMs that applied in the asymmetric encryption can be safely applied as public keys. Simulation results are presented to demonstrate the validity and security of the proposed protocol.

© 2012 OSA

## 1. Introduction

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]

2. 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] [PubMed]

7. J. F. Barrera and R. Torroba, “One step multiplexing optical encryption,” Opt. Commun. **283**(7), 1268–1272 (2010). [CrossRef]

8. T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. **39**(8), 2031–2035 (2000). [CrossRef]

9. H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-phase retrieval for optical security systems by use of random-phase encoding,” Appl. Opt. **41**(23), 4825–4834 (2002). [CrossRef] [PubMed]

10. H. E. Hwang, H. T. Chang, and W. N. Lie, “Fast double-phase retrieval in Fresnel domain using modified Gerchberg-Saxton algorithm for lensless optical security systems,” Opt. Express **17**(16), 13700–13710 (2009). [CrossRef] [PubMed]

11. J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. **35**(21), 3553–3555 (2010). [CrossRef] [PubMed]

15. H. Tashima, M. Takeda, H. Suzuki, T. Obi, M. Yamaguchi, and N. Ohyama, “Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack,” Opt. Express **18**(13), 13772–13781 (2010). [CrossRef] [PubMed]

16. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. **35**(2), 118–120 (2010). [CrossRef] [PubMed]

16. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. **35**(2), 118–120 (2010). [CrossRef] [PubMed]

18. X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. **284**(1), 148–152 (2011). [CrossRef]

19. X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. **284**(19), 4441–4445 (2011). [CrossRef]

20. W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. **13**(7), 075404 (2011). [CrossRef]

21. W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. **284**(16-17), 3913–3917 (2011). [CrossRef]

18. X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. **284**(1), 148–152 (2011). [CrossRef]

21. W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. **284**(16-17), 3913–3917 (2011). [CrossRef]

16. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. **35**(2), 118–120 (2010). [CrossRef] [PubMed]

22. X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. **285**(6), 1078–1081 (2012). [CrossRef]

18. X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. **284**(1), 148–152 (2011). [CrossRef]

21. W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. **284**(16-17), 3913–3917 (2011). [CrossRef]

23. X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. **50**(36), 6645–6651 (2011). [CrossRef] [PubMed]

**35**(2), 118–120 (2010). [CrossRef] [PubMed]

**284**(16-17), 3913–3917 (2011). [CrossRef]

## 2. Double images encryption based on an asymmetric algorithm

*f*system [7

7. J. F. Barrera and R. Torroba, “One step multiplexing optical encryption,” Opt. Commun. **283**(7), 1268–1272 (2010). [CrossRef]

8. T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. **39**(8), 2031–2035 (2000). [CrossRef]

## 3. Analysis of the encryption security

24. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. **21**(15), 2758–2769 (1982). [CrossRef] [PubMed]

22. X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. **285**(6), 1078–1081 (2012). [CrossRef]

**35**(2), 118–120 (2010). [CrossRef] [PubMed]

15. H. Tashima, M. Takeda, H. Suzuki, T. Obi, M. Yamaguchi, and N. Ohyama, “Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack,” Opt. Express **18**(13), 13772–13781 (2010). [CrossRef] [PubMed]

## 4. Numerical simulations and discussion

*m*= 500,

*n*= 100) is illustrated in Fig. 10(e). Obviously, no valuable information about the primary image could be observed. Comparing to PTFT-based single-image encryption, the proposed method provides a good performance in resistance against known public key attack.

## 5. Conclusion

## Acknowledgments

## References and links

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

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

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

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

5. | H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express |

6. | A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. |

7. | J. F. Barrera and R. Torroba, “One step multiplexing optical encryption,” Opt. Commun. |

8. | T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. |

9. | H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-phase retrieval for optical security systems by use of random-phase encoding,” Appl. Opt. |

10. | H. E. Hwang, H. T. Chang, and W. N. Lie, “Fast double-phase retrieval in Fresnel domain using modified Gerchberg-Saxton algorithm for lensless optical security systems,” Opt. Express |

11. | J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. |

12. | 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. |

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

14. | Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express |

15. | H. Tashima, M. Takeda, H. Suzuki, T. Obi, M. Yamaguchi, and N. Ohyama, “Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack,” Opt. Express |

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

17. | W. Stallings, |

18. | X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. |

19. | X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. |

20. | W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt. |

21. | W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. |

22. | X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. |

23. | X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. |

24. | J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. |

25. | S. Yuan, X. Zhou, D. H. Li, and D. F. Zhou, “Simultaneous transmission for an encrypted image and a double random-phase encryption key,” Appl. Opt. |

**OCIS Codes**

(070.4560) Fourier optics and signal processing : Data processing by optical means

(100.2000) Image processing : Digital image processing

**ToC Category:**

Image Processing

**History**

Original Manuscript: February 27, 2012

Revised Manuscript: May 6, 2012

Manuscript Accepted: May 9, 2012

Published: May 11, 2012

**Citation**

Xiaogang Wang and Daomu Zhao, "Double images encryption method with resistance against the specific attack based on an asymmetric algorithm," Opt. Express **20**, 11994-12003 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-11994

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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]
- 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] [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]
- G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett.29(14), 1584–1586 (2004). [CrossRef] [PubMed]
- H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express14(5), 1755–1766 (2006). [CrossRef] [PubMed]
- A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon.1(3), 589–636 (2009). [CrossRef]
- J. F. Barrera and R. Torroba, “One step multiplexing optical encryption,” Opt. Commun.283(7), 1268–1272 (2010). [CrossRef]
- T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng.39(8), 2031–2035 (2000). [CrossRef]
- H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-phase retrieval for optical security systems by use of random-phase encoding,” Appl. Opt.41(23), 4825–4834 (2002). [CrossRef] [PubMed]
- H. E. Hwang, H. T. Chang, and W. N. Lie, “Fast double-phase retrieval in Fresnel domain using modified Gerchberg-Saxton algorithm for lensless optical security systems,” Opt. Express17(16), 13700–13710 (2009). [CrossRef] [PubMed]
- J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett.35(21), 3553–3555 (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]
- Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express15(16), 10253–10265 (2007). [CrossRef] [PubMed]
- H. Tashima, M. Takeda, H. Suzuki, T. Obi, M. Yamaguchi, and N. Ohyama, “Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack,” Opt. Express18(13), 13772–13781 (2010). [CrossRef] [PubMed]
- W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett.35(2), 118–120 (2010). [CrossRef] [PubMed]
- W. Stallings, Cryptography and Network Security: Principles and Practice (Prentice Hall, 2003).
- X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun.284(1), 148–152 (2011). [CrossRef]
- X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun.284(19), 4441–4445 (2011). [CrossRef]
- W. Chen and X. Chen, “Optical asymmetric cryptography using a three-dimensional space-based model,” J. Opt.13(7), 075404 (2011). [CrossRef]
- W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun.284(16-17), 3913–3917 (2011). [CrossRef]
- X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun.285(6), 1078–1081 (2012). [CrossRef]
- X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt.50(36), 6645–6651 (2011). [CrossRef] [PubMed]
- J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21(15), 2758–2769 (1982). [CrossRef] [PubMed]
- S. Yuan, X. Zhou, D. H. Li, and D. F. Zhou, “Simultaneous transmission for an encrypted image and a double random-phase encryption key,” Appl. Opt.46(18), 3747–3753 (2007). [CrossRef] [PubMed]

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