## Double-lock for image encryption with virtual optical wavelength

Optics Express, Vol. 10, Issue 1, pp. 41-45 (2002)

http://dx.doi.org/10.1364/OE.10.000041

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### Abstract

A new method based on the concept of virtual optics for both encryption and decryption is proposed. The technique shows the possibility to encode/decode any digital information. A virtual wavelength and a pseudo-random covering mask (PRCM) are used to design “double locks” and “double keys” for image encryption. Numerical experiments are presented to test the sensitivity of the virtual wavelength. The possible dimensions of keys are roughly estimated and show a high security level.

© Optical Society of America

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

*x*,

_{i}*y*,

_{i}*z*)is a spatial position of reconstructed image point (here a real image is considered) in three-dimensional space, (

_{i}*x*,

_{o}*y*,

_{o}*z*) is a spatial position of object point source, (

_{o}*x*,

_{c}*y*,

_{c}*z*) is a point source of reconstructing wave. The object (i.e. image cover sheet) is a linear superposition of point sources. The wavelength,

_{c}*λ*

_{1}, is a virtual one that we can secretly select to digitally encode hologram, and

*λ*

_{2}is that of being used for reconstruction. A PRCM numerically generated is placed at

*z*, a distance from the PRCM plane to the digital hologram plane in which the origin of Cartesian coordinate system of digital hologram is defined as shown in Fig.1. Suppose that the cascade of host image sheet and random mask is “illuminated” with a virtually coherent wave. Thus, the output signal adjacent PRCM output plane becomes a randomly “scattered light field” and the original image has been converted by the PRCM in this way.

_{PRCM}*ξ*-

*o*-

*η*plane to form an off-axis digital hologram. Decoding digital hologram is numerically performed with a spectrum manipulation algorithm [10

10. L. Yu and L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A , **18**, 1033–1045 (2001). [CrossRef]

*z*direction as shown in Fig. 1. The reconstructed complex distribution at spatial position

*z*=

_{i}*z*is given as the encrypted data, and denoted by

_{o}*C*|

_{z=zi}. By the same procedure, we can also record another digital hologram of the PRCM to prepare a “key-mould” for key fabrication. All the above process use a secretly and arbitrarily selected virtual wavelength (

*λ*

_{1}= 0.623

*μm*). As in the simulations of this paper, the geometric parameters used are:

*z*= 1.2

_{o}*m*,

*z*= 1.1

_{PRCM}*m*. The size of hologram is set to be 6

*mm*by 6

*mm*with 256×256 pixels. Fig.2 (a)-(b) show the original host image, and the converted image with the PRCM. Digital hologram of both the object and the PRCM is recorded by using the arbitrarily selected wavelength (

*λ*

_{1}= 0.623

*μm*), the holograms are shown in Fig. 3 (a)-(b).

*z*=1.2

_{i}*m*is given as Fig. 4(a), where the correct wavelength of 0.623

*μm*is used but without a correct key for PRCM.

^{8})

^{20×20}, which is a huge number. The virtual wavelength will also introduce a huge key dimension because it can be selected from a huge numerical range instead of one coming from physically existed light source. For example, if both the recording and the reconstructing wavelength are randomly selected from a scope between 500

*nm*and 2500

*nm*, and since their sensitivities are around 0.00002

*nm*, thus the possible dimension resulted from the wavelength could be 10

^{16}. So the total key dimension is a huge number and it is really difficult for any digital methods to successfully attack the encrypted information. And comparing the possibility to use real optical system to attack the digitally encoded information, it is even more difficult than digital methods, because even if all the optical parameters and the physical parameters are known, the tolerance of 0.00002nm may be too small to realize or the virtual wavelength may not exit in real world.

## References and Links

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

2. | N. Yoshikawa, M. Itoh, and T. Yatagai, “Binary computer-generated holograms for security applications from a synthetic double-exposure method by electron-beam lithography,” Opt. Lett. |

3. | J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Encrypted holographic data storage based on orthogonal-phase-code multiplexing,” Appl. Opt. |

4. | B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. |

5. | B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. |

6. | S. Lai and M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption”, Opt. Comm. |

7. | O. Matoba and B. Javidi, “Encrypted optical storage with wavelength-key and random phase codes”, Appl. Opt. |

8. | E. Tajahuerce, O. Matoba, S.C. Verrall, and B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry”, Appl. Opt. |

9. | O. Matoba and B. Javidi, “Encrypted Optical Memory Using Multi-Dimensional Keys,” Opt. Lett. |

10. | L. Yu and L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A , |

**OCIS Codes**

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

(090.1760) Holography : Computer holography

(200.3050) Optics in computing : Information processing

**ToC Category:**

Research Papers

**History**

Original Manuscript: December 7, 2001

Published: January 14, 2002

**Citation**

Xiang Peng, Lingfeng Yu, and Lilong Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Express **10**, 41-45 (2002)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-1-41

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### References

- Ph. Refregier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769 (1995). [CrossRef] [PubMed]
- N. Yoshikawa, M. Itoh, and T. Yatagai, "Binary computer-generated holograms for security applications from a synthetic double-exposure method by electron-beam lithography," Opt. Lett. 23, 1483-1485 (1998). [CrossRef]
- J. F. Heanue, M. C. Bashaw, and L. Hesselink, "Encrypted holographic data storage based on orthogonalphase-code multiplexing," Appl. Opt. 34, 6012-6015 (1995). [CrossRef] [PubMed]
- B. Javidi and T. Nomura, "Securing information by use of digital holography," Opt. Lett. 25, 28-30 (2000). [CrossRef]
- B. Javidi and E. Tajahuerce, "Three-dimensional object recognition by use of digital holography," Opt. Lett. 25, 28-30 (2000). [CrossRef]
- S. Lai and M. A. Neifeld, "Digital wavefront reconstruction and its application to image encryption", Opt. Comm. 178, 283-289 (2000). [CrossRef]
- O. Matoba and B. Javidi, "Encrypted optical storage with wavelength-key and random phase codes," Appl. Opt. 38, 6785-90 (1999). [CrossRef]
- E. Tajahuerce, O. Matoba, S.C. Verrall, and B. Javidi, "Optoelectronic information encryption with phaseshifting interferometry," Appl. Opt. 39, 2313-2320 (2000). [CrossRef]
- O. Matoba and B. Javidi, "Encrypted Optical Memory Using Multi-Dimensional Keys," Opt. Lett. 24, 762-765 (1999). [CrossRef]
- L. Yu and L. Cai, "Iterative algorithm with a constraint condition for numerical reconstruction of a threedimensional object from its hologram," J. Opt. Soc. Am. A, 18, 1033-1045 (2001). [CrossRef]

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