Abstract

In this research, a novel optical multiple-image encryption method based on angular-multiplexing holography, quick response (QR) code, and spiral phase keys is proposed. With this method, images are transformed into QR codes and subsequently encrypted into a series of encrypted holograms using an angular-multiplexing technique. The encrypted holograms can only be decrypted when the hologram is illuminated with a duplicate of the reference beam and correct fingerprint and spiral phase plate (SPP) keys. The multiplexing performance and key sensitivity of fingerprint and SPP order were both analyzed, showing the high strength of the security of our proposed method.

© 2019 Optical Society of America

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References

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2019 (2)

L. Sui, X. Zhang, C. Huang, A. Tian, and K. Asundid, “Silhouette-free interference-based multiple-image encryption using cascaded fractional Fourier transforms,” Opt. Lasers Eng. 113, 29–37 (2019).
[Crossref]

L. Sui, X. Zhao, C. Huang, A. Tian, and A. Anand, “An optical multiple-image authentication based on transport of intensity equation,” Opt. Lasers Eng. 116, 116–124 (2019).
[Crossref]

2018 (1)

2017 (4)

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Y. Wei, A. Yan, J. Dong, Z. Hu, and J. Zhang, “Optical image encryption using QR code and multilevel fingerprints in gyrator transform domains,” Opt. Commun. 403, 62–67 (2017).
[Crossref]

D. Xu, M. Lu, C. Jia, and Z. Hu, “Angular-multiplexing optical multiple-image encryption based on digital holography and random amplitude mask,” J. Russ. Laser Res. 38, 1–9 (2017).
[Crossref]

S. Jiao, W. Zou, and X. Li, “QR code based noise-free optical encryption and decryption of a gray scale image,” Opt. Commun. 387, 235–240 (2017).
[Crossref]

2016 (1)

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

2015 (2)

B. Arief, B. A. M. Adzmi, and T. Gross, “Understanding cybercrime from its stakeholders’ perspectives: part 1-attackers,” IEEE Security Privacy 13, 71–76 (2015).
[Crossref]

X. Deng, “Optical image encryption based on real-valued coding and subtracting with the help of QR code,” Opt. Commun. 349, 48–53 (2015).
[Crossref]

2014 (2)

A. Markman, B. Javidi, and M. Tehranipoor, “Photon-counting security tagging and verification using optically encoded QR codes,” IEEE Photon. J. 6, 1–9 (2014).
[Crossref]

S. K. Rajput, D. Kumar, and N. K. Nishchal, “Photon counting imaging and polarized light encoding for secure image verification and hologram watermarking,” J. Opt. 16, 125406 (2014).
[Crossref]

2013 (3)

2011 (1)

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[Crossref]

2010 (1)

2009 (1)

E. Shmueli, R. Vaisenberg, Y. Elovici, and C. Glezer, “Database encryption: an overview of contemporary challenges and design considerations,” ACM SIGMOD Rec. 38, 29–34 (2009).
[Crossref]

2005 (1)

J. Kim, J. Choi, J. An, N. Kim, and K. Lee, “Digital holographic security system based on random phase encoded reference beams and fingerprint identification,” Opt. Commun. 247, 265–274 (2005).
[Crossref]

2004 (2)

2003 (1)

W. Su, C. Sun, and Y. Yang, “Optical encryption and decryption in security-volume holograms,” Proc. SPIE 5206, 177–184 (2003).
[Crossref]

1996 (1)

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
[Crossref]

1995 (1)

Adzmi, B. A. M.

B. Arief, B. A. M. Adzmi, and T. Gross, “Understanding cybercrime from its stakeholders’ perspectives: part 1-attackers,” IEEE Security Privacy 13, 71–76 (2015).
[Crossref]

An, J.

J. Kim, J. Choi, J. An, N. Kim, and K. Lee, “Digital holographic security system based on random phase encoded reference beams and fingerprint identification,” Opt. Commun. 247, 265–274 (2005).
[Crossref]

Anand, A.

L. Sui, X. Zhao, C. Huang, A. Tian, and A. Anand, “An optical multiple-image authentication based on transport of intensity equation,” Opt. Lasers Eng. 116, 116–124 (2019).
[Crossref]

Arief, B.

B. Arief, B. A. M. Adzmi, and T. Gross, “Understanding cybercrime from its stakeholders’ perspectives: part 1-attackers,” IEEE Security Privacy 13, 71–76 (2015).
[Crossref]

Asundid, K.

L. Sui, X. Zhang, C. Huang, A. Tian, and K. Asundid, “Silhouette-free interference-based multiple-image encryption using cascaded fractional Fourier transforms,” Opt. Lasers Eng. 113, 29–37 (2019).
[Crossref]

Barrera, J. F.

Bolognini, N.

Chen, H.

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

Chen, W.

Chen, X.

Cheng, X.

Choi, J.

J. Kim, J. Choi, J. An, N. Kim, and K. Lee, “Digital holographic security system based on random phase encoded reference beams and fingerprint identification,” Opt. Commun. 247, 265–274 (2005).
[Crossref]

Deng, X.

X. Deng, “Optical image encryption based on real-valued coding and subtracting with the help of QR code,” Opt. Commun. 349, 48–53 (2015).
[Crossref]

Ding, J.-P.

Dong, G.

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

Dong, J.

Y. Wei, A. Yan, J. Dong, Z. Hu, and J. Zhang, “Optical image encryption using QR code and multilevel fingerprints in gyrator transform domains,” Opt. Commun. 403, 62–67 (2017).
[Crossref]

Elovici, Y.

E. Shmueli, R. Vaisenberg, Y. Elovici, and C. Glezer, “Database encryption: an overview of contemporary challenges and design considerations,” ACM SIGMOD Rec. 38, 29–34 (2009).
[Crossref]

Glezer, C.

E. Shmueli, R. Vaisenberg, Y. Elovici, and C. Glezer, “Database encryption: an overview of contemporary challenges and design considerations,” ACM SIGMOD Rec. 38, 29–34 (2009).
[Crossref]

Gong, Q.

Gross, T.

B. Arief, B. A. M. Adzmi, and T. Gross, “Understanding cybercrime from its stakeholders’ perspectives: part 1-attackers,” IEEE Security Privacy 13, 71–76 (2015).
[Crossref]

Guo, C.-S.

He, W.

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

Hu, Z.

Y. Wei, A. Yan, J. Dong, Z. Hu, and J. Zhang, “Optical image encryption using QR code and multilevel fingerprints in gyrator transform domains,” Opt. Commun. 403, 62–67 (2017).
[Crossref]

D. Xu, M. Lu, C. Jia, and Z. Hu, “Angular-multiplexing optical multiple-image encryption based on digital holography and random amplitude mask,” J. Russ. Laser Res. 38, 1–9 (2017).
[Crossref]

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Huang, C.

L. Sui, X. Zhang, C. Huang, A. Tian, and K. Asundid, “Silhouette-free interference-based multiple-image encryption using cascaded fractional Fourier transforms,” Opt. Lasers Eng. 113, 29–37 (2019).
[Crossref]

L. Sui, X. Zhao, C. Huang, A. Tian, and A. Anand, “An optical multiple-image authentication based on transport of intensity equation,” Opt. Lasers Eng. 116, 116–124 (2019).
[Crossref]

Ishii, N.

Javidi, B.

A. Markman, B. Javidi, and M. Tehranipoor, “Photon-counting security tagging and verification using optically encoded QR codes,” IEEE Photon. J. 6, 1–9 (2014).
[Crossref]

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

Jia, C.

D. Xu, M. Lu, C. Jia, and Z. Hu, “Angular-multiplexing optical multiple-image encryption based on digital holography and random amplitude mask,” J. Russ. Laser Res. 38, 1–9 (2017).
[Crossref]

Jiao, S.

S. Jiao, W. Zou, and X. Li, “QR code based noise-free optical encryption and decryption of a gray scale image,” Opt. Commun. 387, 235–240 (2017).
[Crossref]

Katano, Y.

Kim, J.

J. Kim, J. Choi, J. An, N. Kim, and K. Lee, “Digital holographic security system based on random phase encoded reference beams and fingerprint identification,” Opt. Commun. 247, 265–274 (2005).
[Crossref]

Kim, N.

J. Kim, J. Choi, J. An, N. Kim, and K. Lee, “Digital holographic security system based on random phase encoded reference beams and fingerprint identification,” Opt. Commun. 247, 265–274 (2005).
[Crossref]

Kinoshita, N.

Kumar, D.

S. K. Rajput, D. Kumar, and N. K. Nishchal, “Photon counting imaging and polarized light encoding for secure image verification and hologram watermarking,” J. Opt. 16, 125406 (2014).
[Crossref]

Lai, S.

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
[Crossref]

Lee, K.

J. Kim, J. Choi, J. An, N. Kim, and K. Lee, “Digital holographic security system based on random phase encoded reference beams and fingerprint identification,” Opt. Commun. 247, 265–274 (2005).
[Crossref]

Li, G.

Li, X.

S. Jiao, W. Zou, and X. Li, “QR code based noise-free optical encryption and decryption of a gray scale image,” Opt. Commun. 387, 235–240 (2017).
[Crossref]

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

Liu, J.

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[Crossref]

Liu, X.

Lu, M.

D. Xu, M. Lu, C. Jia, and Z. Hu, “Angular-multiplexing optical multiple-image encryption based on digital holography and random amplitude mask,” J. Russ. Laser Res. 38, 1–9 (2017).
[Crossref]

Markman, A.

A. Markman, B. Javidi, and M. Tehranipoor, “Photon-counting security tagging and verification using optically encoded QR codes,” IEEE Photon. J. 6, 1–9 (2014).
[Crossref]

Meng, X.

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

Mira, A.

Muroi, T.

Nishchal, N. K.

S. K. Rajput, D. Kumar, and N. K. Nishchal, “Photon counting imaging and polarized light encoding for secure image verification and hologram watermarking,” J. Opt. 16, 125406 (2014).
[Crossref]

Nobukawa, T.

Peng, X.

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

Poon, T. C.

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Qin, Y.

Rajput, S. K.

S. K. Rajput, D. Kumar, and N. K. Nishchal, “Photon counting imaging and polarized light encoding for secure image verification and hologram watermarking,” J. Opt. 16, 125406 (2014).
[Crossref]

Refregier, P.

Ren, X.-Y.

Sheppard, C. J. R.

Shmueli, E.

E. Shmueli, R. Vaisenberg, Y. Elovici, and C. Glezer, “Database encryption: an overview of contemporary challenges and design considerations,” ACM SIGMOD Rec. 38, 29–34 (2009).
[Crossref]

Situ, G.

Su, W.

W. Su, C. Sun, and Y. Yang, “Optical encryption and decryption in security-volume holograms,” Proc. SPIE 5206, 177–184 (2003).
[Crossref]

Sui, L.

L. Sui, X. Zhao, C. Huang, A. Tian, and A. Anand, “An optical multiple-image authentication based on transport of intensity equation,” Opt. Lasers Eng. 116, 116–124 (2019).
[Crossref]

L. Sui, X. Zhang, C. Huang, A. Tian, and K. Asundid, “Silhouette-free interference-based multiple-image encryption using cascaded fractional Fourier transforms,” Opt. Lasers Eng. 113, 29–37 (2019).
[Crossref]

Sun, C.

W. Su, C. Sun, and Y. Yang, “Optical encryption and decryption in security-volume holograms,” Proc. SPIE 5206, 177–184 (2003).
[Crossref]

Tebaldi, M.

Tehranipoor, M.

A. Markman, B. Javidi, and M. Tehranipoor, “Photon-counting security tagging and verification using optically encoded QR codes,” IEEE Photon. J. 6, 1–9 (2014).
[Crossref]

Tian, A.

L. Sui, X. Zhang, C. Huang, A. Tian, and K. Asundid, “Silhouette-free interference-based multiple-image encryption using cascaded fractional Fourier transforms,” Opt. Lasers Eng. 113, 29–37 (2019).
[Crossref]

L. Sui, X. Zhao, C. Huang, A. Tian, and A. Anand, “An optical multiple-image authentication based on transport of intensity equation,” Opt. Lasers Eng. 116, 116–124 (2019).
[Crossref]

Torroba, R.

Tsang, P. W. M.

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Vaisenberg, R.

E. Shmueli, R. Vaisenberg, Y. Elovici, and C. Glezer, “Database encryption: an overview of contemporary challenges and design considerations,” ACM SIGMOD Rec. 38, 29–34 (2009).
[Crossref]

Vargas, C.

Wang, H.-T.

Wang, Y.

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[Crossref]

Wei, Y.

Y. Wei, A. Yan, J. Dong, Z. Hu, and J. Zhang, “Optical image encryption using QR code and multilevel fingerprints in gyrator transform domains,” Opt. Commun. 403, 62–67 (2017).
[Crossref]

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Weng, D.

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[Crossref]

Xie, J.

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[Crossref]

Xu, D.

D. Xu, M. Lu, C. Jia, and Z. Hu, “Angular-multiplexing optical multiple-image encryption based on digital holography and random amplitude mask,” J. Russ. Laser Res. 38, 1–9 (2017).
[Crossref]

Yan, A.

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Y. Wei, A. Yan, J. Dong, Z. Hu, and J. Zhang, “Optical image encryption using QR code and multilevel fingerprints in gyrator transform domains,” Opt. Commun. 403, 62–67 (2017).
[Crossref]

Yang, X.

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

Yang, Y.

W. Su, C. Sun, and Y. Yang, “Optical encryption and decryption in security-volume holograms,” Proc. SPIE 5206, 177–184 (2003).
[Crossref]

Yin, Y.

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

Zhang, J.

Y. Wei, A. Yan, J. Dong, Z. Hu, and J. Zhang, “Optical image encryption using QR code and multilevel fingerprints in gyrator transform domains,” Opt. Commun. 403, 62–67 (2017).
[Crossref]

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

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

Zhang, X.

L. Sui, X. Zhang, C. Huang, A. Tian, and K. Asundid, “Silhouette-free interference-based multiple-image encryption using cascaded fractional Fourier transforms,” Opt. Lasers Eng. 113, 29–37 (2019).
[Crossref]

Zhao, X.

L. Sui, X. Zhao, C. Huang, A. Tian, and A. Anand, “An optical multiple-image authentication based on transport of intensity equation,” Opt. Lasers Eng. 116, 116–124 (2019).
[Crossref]

Zhu, N.

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[Crossref]

Zou, W.

S. Jiao, W. Zou, and X. Li, “QR code based noise-free optical encryption and decryption of a gray scale image,” Opt. Commun. 387, 235–240 (2017).
[Crossref]

ACM SIGMOD Rec. (1)

E. Shmueli, R. Vaisenberg, Y. Elovici, and C. Glezer, “Database encryption: an overview of contemporary challenges and design considerations,” ACM SIGMOD Rec. 38, 29–34 (2009).
[Crossref]

Appl. Opt. (1)

IEEE Photon. J. (2)

X. Li, X. Meng, X. Yang, Y. Yin, Y. Wang, X. Peng, W. He, G. Dong, and H. Chen, “Multiple-image encryption based on compressive ghost imaging and coordinate sampling,” IEEE Photon. J. 8, 390051 (2016).
[Crossref]

A. Markman, B. Javidi, and M. Tehranipoor, “Photon-counting security tagging and verification using optically encoded QR codes,” IEEE Photon. J. 6, 1–9 (2014).
[Crossref]

IEEE Security Privacy (1)

B. Arief, B. A. M. Adzmi, and T. Gross, “Understanding cybercrime from its stakeholders’ perspectives: part 1-attackers,” IEEE Security Privacy 13, 71–76 (2015).
[Crossref]

J. Opt. (1)

S. K. Rajput, D. Kumar, and N. K. Nishchal, “Photon counting imaging and polarized light encoding for secure image verification and hologram watermarking,” J. Opt. 16, 125406 (2014).
[Crossref]

J. Russ. Laser Res. (1)

D. Xu, M. Lu, C. Jia, and Z. Hu, “Angular-multiplexing optical multiple-image encryption based on digital holography and random amplitude mask,” J. Russ. Laser Res. 38, 1–9 (2017).
[Crossref]

Opt. Commun. (5)

D. Weng, N. Zhu, Y. Wang, J. Xie, and J. Liu, “Experimental verification of optical image encryption based on interference,” Opt. Commun. 284, 2485–2487 (2011).
[Crossref]

S. Jiao, W. Zou, and X. Li, “QR code based noise-free optical encryption and decryption of a gray scale image,” Opt. Commun. 387, 235–240 (2017).
[Crossref]

X. Deng, “Optical image encryption based on real-valued coding and subtracting with the help of QR code,” Opt. Commun. 349, 48–53 (2015).
[Crossref]

J. Kim, J. Choi, J. An, N. Kim, and K. Lee, “Digital holographic security system based on random phase encoded reference beams and fingerprint identification,” Opt. Commun. 247, 265–274 (2005).
[Crossref]

Y. Wei, A. Yan, J. Dong, Z. Hu, and J. Zhang, “Optical image encryption using QR code and multilevel fingerprints in gyrator transform domains,” Opt. Commun. 403, 62–67 (2017).
[Crossref]

Opt. Eng. (1)

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (2)

L. Sui, X. Zhang, C. Huang, A. Tian, and K. Asundid, “Silhouette-free interference-based multiple-image encryption using cascaded fractional Fourier transforms,” Opt. Lasers Eng. 113, 29–37 (2019).
[Crossref]

L. Sui, X. Zhao, C. Huang, A. Tian, and A. Anand, “An optical multiple-image authentication based on transport of intensity equation,” Opt. Lasers Eng. 116, 116–124 (2019).
[Crossref]

Opt. Lett. (5)

Proc. SPIE (1)

W. Su, C. Sun, and Y. Yang, “Optical encryption and decryption in security-volume holograms,” Proc. SPIE 5206, 177–184 (2003).
[Crossref]

Sci. Rep. (1)

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. Proposed optical holographic encryption and decryption system. HWP, half-wave plate; M, mirror; L, lens; PBS, polarizing beam splitter; BE, beam expander; FP, fingerprint key; SPP, spiral phase plate; LN, lithium niobate crystal; AF, attenuator; CCD, charge-coupled device.
Fig. 2.
Fig. 2. (a) Original binary image; (b) QR code transformed from the original image shown in (a); (c) SPP ( l = 5 ); (d) fingerprint for encryption; (e) encrypted hologram from the QR code shown in (b); (f) another original image; (g) QR code transformed from the original image shown in (f); and (h) encrypted hologram from the QR code shown in (g).
Fig. 3.
Fig. 3. (a) Decrypted QR code with correct keys; (b) wrong fingerprint for decryption; (c) decrypted QR code with wrong fingerprint shown in (b); (d) wrong key of SPP ( l = 8 ); and (e) decrypted QR code with wrong key shown in (d).
Fig. 4.
Fig. 4. (a)–(d) Fingerprints of different occlusion areas, and (e)–(h) the decrypted QR code based on the occluded QR codes shown in (a)–(d).
Fig. 5.
Fig. 5. Variation in the CC values with variation in SPP order.
Fig. 6.
Fig. 6. Experimental results. (a) QR code decrypted with all correct keys, (b) QR code decrypted with only the key of SPP ( l = 5 ) but wrong fingerprint, and (c) QR code decrypted with only the key of the fingerprint but the wrong SPP.
Fig. 7.
Fig. 7. Experimental results. (a) QR code decrypted with all correct keys, (b) QR code decrypted with only the key of SPP ( l = 5 ) but wrong fingerprint, and (c) QR code decrypted with only the key of the fingerprint but the wrong SPP.
Fig. 8.
Fig. 8. Decrypted images with correct keys but the deviation angle (a)  Δ θ = 0.01 ° , (b) 0.02°, and (c) 0.03° of the readout reference beam.
Fig. 9.
Fig. 9. Decrypted images with correct fingerprint but incorrect SPP order (a)  l = 2 , (b) 3, (c) 4, (d) 6, (e) 7, and (f) 8.

Equations (3)

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p ( x , y ) = exp ( i l θ ) ,
h ( x , y ) = | o ( x , y ) | 2 + | r ( x , y ) | 2 + o ( x , y ) r * ( x , y ) + o * ( x , y ) r ( x , y ) ,
CC = x y ( O x , y O ) ( O x , y O ¯ ) [ x y ( O x , y O ¯ ) 2 ] [ x y ( O x , y O ¯ ) 2 ] ,

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