Scientific Research

An Academic Publisher

**Information Encryption Based on Using Arbitrary Two-Step Phase-Shift Interferometry** ()

A deterministic phase-encoded encryption system is proposed. A lenticular lens array (LLA) sheet with a particular LPI (lenticular per inch) number is chosen as a modulator (key) instead of the random phase molator. The suggested encryption scheme is based on arbitrary two-step phase-shift interferometry (PSI), using an unknown phase step. The encryption and decryption principle is based on an LLA in arbitrary unknown two-step PSI. Right key holograms can be used to theoretically show that the object wavefront is the only one left in the hologram plane and that all accompanying undesired terms are eliminated. The encrypted image can therefore be numerically and successfully decrypted with the right key in the image plane. The number of degrees of freedom of the encryption scheme increases with the distance from the object and the LLA to the CCD, and also with the unknown phase-step and the LLA LPI number. Computer simulations are performed to verify the encryption and decryption principles without a key, with the wrong key and with the right key. Optical experiments are also performed to validate them.

Keywords

Share and Cite:

C. Chang, W. Wu, M. Shiu, W. Hsieh, J. Wang and H. Yau, "Information Encryption Based on Using Arbitrary Two-Step Phase-Shift Interferometry,"

*Optics and Photonics Journal*, Vol. 1 No. 4, 2011, pp. 204-215. doi: 10.4236/opj.2011.14032.Conflicts of Interest

The authors declare no conflicts of interest.

[1] | J. W. Goodman and R. W. Lawrence, “Digital Image Formation from Electronically Detected Hologram,” Applied Physics Letters, Vol. 11, No. 3, 1967, pp. 77-79. doi:10.1063/1.1755043 |

[2] | U. Schnars and W. Juptner, “Direct Recording of Holograms by a CCD Target and Numerical Reconstruction,” Applied Optics, Vol. 33, No. 2, 1994, pp. 179-181. doi:10.1364/AO.33.000179 |

[3] | I. Yamaguchi and T. Zhang, “Phase-Shifting Digital Holography,” Optics Letters, Vol. 22, No. 16, 1997, pp. 1268-1270. doi:10.1364/OL.22.001268 |

[4] | B. Javidi, G. Zhang and J. Li, “Experimental Demonstration of the Random Phase Encoding Technique for Image Encryption and Security Verification,” Optical Engineering, Vol. 35, No. 9, 1996, pp. 2506-2512. doi:10.1117/1.600854 |

[5] | B. Javidi and T. Nomura, “Securing Information by Use of Digital Holography,” Optics Letters, Vol. 25, No. 1, 2000, pp. 28-30. doi:10.1364/OL.25.000028 |

[6] | E. Tajahuerce, O. Matoba, S. C. Verrall and B. Javidi, “Optoelectronic Information Encryption with Phase-Shifting Interferometry,” Applied Optics, Vol. 39, No. 14, 2000, pp. 2313-2320. doi:10.1364/AO.39.002313 |

[7] | E. Tajahuerce and B. Javidi, “Encrypting Three-Dimen- sional Information with Digital Holography,” Applied Optics, Vol. 39, No. 35, 2000, pp. 6595-6601. doi:10.1364/AO.39.006595 |

[8] | S. Lai and M. A. Neifeld, “Digital Wavefront Reconstruction and Its Application to Image Encryption,” Optics Communications, Vol. 178, No. 4-6, 2000, pp. 283- 289. doi:10.1016/S0030-4018(00)00641-6 |

[9] | E. Tajahuerce, J. Lancis, B. Javidi and P. Andres, “Optical Security and Encryption with Totally Incoherent Light,” Optics Letters, Vol. 26, No. 10, 2001, pp. 678- 680. doi:10.1364/OL.26.000678 |

[10] | B. M. Hennelly, J. T. Sheridan, “Image Encryption and The Fractional Fourier Transform,” Optik, Vol. 114, No. 6, 2003, pp. 251-265. doi:10.1078/0030-4026-00257 |

[11] | R. Arizaga., R. Henao, R. Torroba, “Fully Digital Encryption Technique,” Optics Communications, Vol. 221, No. 1-3, 2003, pp. 43-47. doi:10.1016/S0030-4018(03)01462-7 |

[12] | L. Z. Cai, M. Z. He, Q. Liu, and X. L. Yang, “Digital Image Encryption and Watermarking by Phase-Shifting Interferometry,” Applied Optics, Vol. 43, No. 15, 2004, pp. 3078-3084. doi:10.1364/AO.43.003078 |

[13] | N. K. Nishchal, J. Joseph and K. Singh, “Fully Phase Encryption Using Digital Holography,” Optical Engineering, Vol. 43 No. 12, 2004, pp. 2959-2966. doi:10.1117/1.1811085 |

[14] | T. J. Naughton and B. Javidi, “Compression of Encrypted Three-Dimensional Objects Using Digital Holography,” Optical Engineering, Vol. 43, No. 10, 2004, pp. 2233- 2238. doi:10.1117/1.1783280 |

[15] | A. Carnicer, M. M.-Usategui, S. Arcos, and I. Juvells, “Vulnerability to Chosen-Cyphertext Attacks of Optical Encryption Schemes Based on Double Random Phase Keys,” Optics Letters, Vol. 30, No. 13, 2005, pp. 1644- 1646. doi:10.1364/OL.30.001644 |

[16] | L. Chen and D. Zhao, “Optical Image Encryption with Hartley Transforms,” Optics Letters, Vol. 31, No. 23, 2006, pp. 3438-3440. doi:10.1364/OL.31.003438 |

[17] | X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong and Y. R. Wang, “Two-Step Phase-Shifting Interferometry and Its Application in Image Encryption,” Optics Letters, Vol. 31, No. 10, 2006, pp. 1414-1416. doi:10.1364/OL.31.001414 |

[18] | X. Peng, H. H. Wei and P. Zhang, “Chosen-Plaintext Attack on Lensless Double-Random Phase Encoding in the Fresnel Domain,” Optics Letters, Vol. 31, No. 22, 2006, pp. 3261-3263. doi:10.1364/OL.31.003261 |

[19] | 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,” Optics Letters, Vol. 33, No. 14, 2008, pp. 1575-1577. doi:10.1364/OL.33.001575 |

[20] | X. F. Meng, L. H. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong and H. Zhang, “Full-Phase Image Encryption by Two-Step Phase-Shifting Interferometry,” Optik, Vol. 119, No. 9, 2008, pp. 434-440. doi:10.1016/j.ijleo.2007.02.003 |

[21] | A. Nelleri, J. Joseph and K. Singh, “Lensless Complex Data Encoding for Digital Holographic Whole Information Security,” Optical Engineering, Vol. 47, No. 11, 2008, pp. 115801-115809. doi:10.1117/1.3028351 |

[22] | G. L. Chen, W. K. Yang, J. C. Wang and C. C. Chang, “Deterministic Phase Encoding Encryption in Single Shot Digital Holography,” Applied Physics B, Vol. 93, No. 2-3, 2008, pp. 473-479. doi:10.1007/s00340-008-3201-5 |

[23] | Y. Zhang and B. Wang, “Optical Image Encryption Based on Interference,” Optics Letters, Vol. 33, No. 21, 2008, pp. 2443-2445. doi:10.1364/OL.33.002443 |

[24] | Y. L. Xiao, X. Zhou, Q. H. Wang, S. Yuan, and Y. Y. Chen, “Optical Image Encryption Topology,” Optics Letters, Vol. 34, No. 20, 2009, pp. 3223-3225. doi:10.1364/OL.34.003223 |

[25] | O. Matoba, E. Tajahuerce, E. Perez-Cabre, M. S. Millan and B. Javidi, “Optical Techniques for Information Security,” Proceedings of the IEEE, Vol. 97, No. 6, 2009, pp. 1128-1148. doi:10.1109/JPROC.2009.2018367 |

[26] | W. T. Hsieh, M. K. Kuo, H. F. Yau and C. C. Chang, “A Simple Arbitrary Phase-Step Digital Holographic Reconstruction Approach without Blurring Using Two Holograms,” Optical Review, Vol. 16, No. 4, 2009, pp. 466- 471. doi:10.1007/s10043-009-0090-8 |

[27] | R. B. Johnson and G. A. Jacobsen, “Advances in Lenticular Lens Arrays for Visual Display,” Proceedings of SPIE, Current Developments in Lens Design and Optical Engineering VI, San Diego, 2-4 August 2005, paper No. 5874-06. |

[28] | C. C. Chang, G. L. Chen, W. K. Yang, C. Y. Lin, H. F. Yau, “Deterministic Phase Encoded Holographic Data Storage Using Lenticular Lens Array,” Optical Review, Vol. 14, No. 4, 2007, pp. 214-218. doi:10.1007/s10043-007-0214-y |

[29] | T. C. Poon and P. P. Banerjee, “Contemporary Optical Image Processing with MATLAB,” Elsevier, New York, 2001, pp. 4-6. |

[30] | “Pacur Lenstar Lenticular,” 2005. http://www.pacur.com/pdf/lenstar.pdf |

[31] | J. W. Goodman, “Introduction to Fourier Optics,” 2nd Edition, McGraw-Hill, Singapore, 1996, pp. 66-67. |

[32] | Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid Holographic Microscopy Free of Conjugate and Zero-Order Images,” Applied Optics, Vol. 23, No. 15, 1999, pp. 4990-4996. doi:10.1364/AO.38.004990 |

[33] | U. Schnars and W. Juptner, “Digital Recording and Numerical Reconstruction of Holograms,” Measurement Science and Technology, Vol. 13, No. 9, 2002, pp. R85- R101. doi:10.1088/0957-0233/13/9/201 |

[34] | W. K. Pratt, “Digital Image Processing,” 4th Edition, Wiley, New York, 2007, pp. 759-760. doi:10.1002/9780470097434.app3 |

Copyright © 2020 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.