Abstract

An asymmetric multi-image encryption system based on the chirp z-transform (CZT) is demonstrated. The setup is a hybrid architecture that combines a double-random-phase encryption scheme in 4f configuration and a multiplexing procedure based on the CZT. The setup allows encodement of multiple images and their transmittal in a single multiplexed element. The decryption stage has a compact design that allows retrieval of several data without cross-talk noise. Since the system is asymmetric, the users’ decryption keys are different from those used in the encryption process, resulting in an encoding scheme resistant to cryptanalysis attacks. It is demonstrated that multiplexing based on the CZT allows functionality expansion of the static encoding setups (optical, digital or hybrid) to a dynamic range, a fact that provides a versatile solution to handle large volumes of encrypted data efficiently and safely. The viability of this proposal is verified using virtual optical systems.

© 2019 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (1)

E. Mosso and N. Bolognini, “Dynamic multiple-image encryption based on chirp z-transform,” J. Opt. 21, 035704 (2019).
[Crossref]

2018 (1)

R. Kumar, J. T. Sheridan, and B. Bhaduri, “Nonlinear double image encryption using 2d non-separable linear canonical transform and phase retrieval algorithm,” Opt. Laser Technol. 107, 353–360 (2018).
[Crossref]

2017 (2)

2016 (3)

I. Moon, F. Yi, M. Han, and J. Lee, “Efficient asymmetric image authentication schemes based on photon counting-double random phase encoding and RSA algorithms,” Appl. Opt. 55, 4328–4335 (2016).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

E. F. Mosso, N. Bolognini, and D. G. Pérez, “Single-random phase encoding architecture using a focus tunable lens,” J. Opt. 18, 025701 (2016).
[Crossref]

2015 (3)

2014 (3)

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6, 120–155 (2014).
[Crossref]

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Security analysis of phase-only DRPE based on known-plaintext attack using multiple known plaintext-ciphertext pairs,” Appl. Opt. 53, 6435–6443 (2014).
[Crossref]

L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4, 7441 (2014).
[Crossref]

2013 (1)

F. Mosso, E. Peters, N. Bolognini, M. Tebaldi, R. Torroba, and D. G. Pérez, “Experimental imaging coding system using three-dimensional subjective speckle structures,” J. Opt. 15, 125403 (2013).
[Crossref]

2012 (1)

2011 (3)

2010 (1)

2006 (3)

2005 (2)

2000 (1)

1997 (1)

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[Crossref]

1995 (1)

1982 (1)

D. R. R. Reddy and V. Rao, “Two-dimensional chirp z-transform,” Signal Process. 4, 17–24 (1982).
[Crossref]

Abuturab, M. R.

M. R. Abuturab, “An asymmetric single-channel color image encryption based on Hartley transform and gyrator transform,” Opt. Lasers Eng. 69, 49–57 (2015).
[Crossref]

Alfalou, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Arcos, S.

Aumasson, J.-P.

J.-P. Aumasson, Serious Cryptography: A Practical Introduction to Modern Encryption (No Starch, 2018).

Barrera, J. F.

Barrera Ramírez, J. F.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Bhaduri, B.

R. Kumar, J. T. Sheridan, and B. Bhaduri, “Nonlinear double image encryption using 2d non-separable linear canonical transform and phase retrieval algorithm,” Opt. Laser Technol. 107, 353–360 (2018).
[Crossref]

Bolognini, N.

E. Mosso and N. Bolognini, “Dynamic multiple-image encryption based on chirp z-transform,” J. Opt. 21, 035704 (2019).
[Crossref]

E. F. Mosso, N. Bolognini, and D. G. Pérez, “Single-random phase encoding architecture using a focus tunable lens,” J. Opt. 18, 025701 (2016).
[Crossref]

F. Mosso, E. Peters, N. Bolognini, M. Tebaldi, R. Torroba, and D. G. Pérez, “Experimental imaging coding system using three-dimensional subjective speckle structures,” J. Opt. 15, 125403 (2013).
[Crossref]

F. Mosso, M. Tebaldi, J. F. Barrera, N. Bolognini, and R. Torroba, “Pure optical dynamical color encryption,” Opt. Express 19, 13779–13786 (2011).
[Crossref]

F. Mosso, J. F. Barrera, M. Tebaldi, N. Bolognini, and R. Torroba, “All-optical encrypted movie,” Opt. Express 19, 5706–5712 (2011).
[Crossref]

E. Mosso, O. Suárez, and N. Bolognini, “Multiple images decrypted from a multiplexed package,” figshare (2019).

Brosseau, C.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Carnicer, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

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, 1644–1646 (2005).
[Crossref]

Chang, J.

Chen, L.

Chen, W.

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6, 120–155 (2014).
[Crossref]

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

Chen, X.

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6, 120–155 (2014).
[Crossref]

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

Chiou, A. E. T.

Guibert, L.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[Crossref]

Guo, C.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Han, M.

He, W.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

X. Liu, J. Wu, W. He, M. Liao, C. Zhang, and X. Peng, “Vulnerability to ciphertext-only attack of optical encryption scheme based on double random phase encoding,” Opt. Express 23, 18955–18968 (2015).
[Crossref]

He, Y.

Huang, S.

Javidi, B.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6, 120–155 (2014).
[Crossref]

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[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]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, Optical Techniques for Information Security (IEEE, 2009), Vol. 97.

Juvells, I.

Kumar, R.

R. Kumar, J. T. Sheridan, and B. Bhaduri, “Nonlinear double image encryption using 2d non-separable linear canonical transform and phase retrieval algorithm,” Opt. Laser Technol. 107, 353–360 (2018).
[Crossref]

Lee, J.

Lee, S.

J. Leger and S. Lee, "Signal Processing Using Hybrid Systems," in Application of Optical Fourier Transforms, H. Stark, ed. (Academic, 1982), Chap. 4, pp. 141–207.

Leger, J.

J. Leger and S. Lee, "Signal Processing Using Hybrid Systems," in Application of Optical Fourier Transforms, H. Stark, ed. (Academic, 1982), Chap. 4, pp. 141–207.

Liao, M.

Liu, X.

Markman, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Matoba, O.

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, Optical Techniques for Information Security (IEEE, 2009), Vol. 97.

Millán, M.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Millán, M. S.

M. S. Millán and E. Pérez-Cabré, "Optical Data Encryption," in Optical and Digital Image Processing, G. Cristobal, , P. Schelkens, and H. Thienpont, eds. (Wiley, 2011), Chap. 33, pp. 739–767.

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, Optical Techniques for Information Security (IEEE, 2009), Vol. 97.

Montes-Usategui, M.

Moon, I.

Mosso, E.

E. Mosso and N. Bolognini, “Dynamic multiple-image encryption based on chirp z-transform,” J. Opt. 21, 035704 (2019).
[Crossref]

E. Mosso, O. Suárez, and N. Bolognini, “Multiple images decrypted from a multiplexed package,” figshare (2019).

Mosso, E. F.

E. F. Mosso, N. Bolognini, and D. G. Pérez, “Single-random phase encoding architecture using a focus tunable lens,” J. Opt. 18, 025701 (2016).
[Crossref]

Mosso, F.

Nakano, K.

Naruse, M.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Nishchal, N. K.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
[Crossref]

Nomura, T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, Optical Techniques for Information Security (IEEE, 2009), Vol. 97.

Peng, X.

Pérez, D. G.

E. F. Mosso, N. Bolognini, and D. G. Pérez, “Single-random phase encoding architecture using a focus tunable lens,” J. Opt. 18, 025701 (2016).
[Crossref]

F. Mosso, E. Peters, and D. G. Pérez, “Complex wavefront reconstruction from multiple-image planes produced by a focus tunable lens,” Opt. Lett. 40, 4623–4626 (2015).
[Crossref]

F. Mosso, E. Peters, N. Bolognini, M. Tebaldi, R. Torroba, and D. G. Pérez, “Experimental imaging coding system using three-dimensional subjective speckle structures,” J. Opt. 15, 125403 (2013).
[Crossref]

Pérez-Cabré, E.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millán, and B. Javidi, Optical Techniques for Information Security (IEEE, 2009), Vol. 97.

M. S. Millán and E. Pérez-Cabré, "Optical Data Encryption," in Optical and Digital Image Processing, G. Cristobal, , P. Schelkens, and H. Thienpont, eds. (Wiley, 2011), Chap. 33, pp. 739–767.

Peters, E.

F. Mosso, E. Peters, and D. G. Pérez, “Complex wavefront reconstruction from multiple-image planes produced by a focus tunable lens,” Opt. Lett. 40, 4623–4626 (2015).
[Crossref]

F. Mosso, E. Peters, N. Bolognini, M. Tebaldi, R. Torroba, and D. G. Pérez, “Experimental imaging coding system using three-dimensional subjective speckle structures,” J. Opt. 15, 125403 (2013).
[Crossref]

Qin, W.

Rajput, S. K.

Rao, V.

D. R. R. Reddy and V. Rao, “Two-dimensional chirp z-transform,” Signal Process. 4, 17–24 (1982).
[Crossref]

Reddy, D. R. R.

D. R. R. Reddy and V. Rao, “Two-dimensional chirp z-transform,” Signal Process. 4, 17–24 (1982).
[Crossref]

Refregier, P.

Rivenson, Y.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Sergent, A.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[Crossref]

Sheridan, J.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Sheridan, J. T.

R. Kumar, J. T. Sheridan, and B. Bhaduri, “Nonlinear double image encryption using 2d non-separable linear canonical transform and phase retrieval algorithm,” Opt. Laser Technol. 107, 353–360 (2018).
[Crossref]

Situ, G.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera Ramírez, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. Sheridan, G. Situ, M. Naruse, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A 8, 391–397 (2006).
[Crossref]

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Supplementary Material (1)

NameDescription
» Visualization 1       Decrypted sequences from a multiplexed package obtained with an asymmetric multiple-image encryption system based on chirp z-transform. Each decryption uses different combinations of private and public keys.

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Figures (6)

Fig. 1.
Fig. 1. Asymmetric multi-image encryption system based on CZT. Encryption stage: (a) optical scheme of a DRPE4f, (b) digital step based on CZT and Fourier transform, (c) digital multiplexing of encrypted data, and (d) decryption stage based on a 4f coherent processor.
Fig. 2.
Fig. 2. Order of the positioning of the multiplexed information corresponding to the image number (a) 2, (b) 4, (c) 8, (d) 16, (e) 32, and (f) 64 of the original sequence.
Fig. 3.
Fig. 3. Decrypted frame from a multiplexed package by using the combination of the masks χ(k,l) and ζi(w,s) shown in Table 2 (see Visualization 1, [33]).
Fig. 4.
Fig. 4. Decrypted images by using legitimate masks χ(k,l) and ζi(w,s). (a)–(f) are the frames of the dynamic sequence 2, 4, 8, 16, 32, and 64, respectively.
Fig. 5.
Fig. 5. Decrypted images from a multiplexed package by using keys obtained from (a) a CPA and (b) a KPA.
Fig. 6.
Fig. 6. Quality of decrypted images. Marker (asterisk): the intruder has entire possession of χ(k,l) and partially intercepts ζi(w,s). Marker (solid circle) and (×): the intruder has entire possession of ζi(w,s) and partially intercepts χ(k,l). The user decrypts data from a package Mt of 1 and 64 multiplexed images, respectively.

Tables (3)

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Table 1. Spatial Frequency Values Used in the Complex Exponentials A1, A2, W1, and W2

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Table 2. Combination of Legitimate and Illegitimate Keys Used to Decode the Images Shown in Figs. 3(a)3(d), Respectively (see Visualization 1, [33])

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Table 3. Security of the Proposed Encryption System

Equations (6)

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Ei(k,l)=I{I[Ii(m,n)Φ0(m,n)]}I[Φi(u,v)],
X(p,q)=czt[Ei(k,l)]=W1p2/2W2q2/2k=0K1l=0L1g(k,l)W1(pk)2/2W2(ql)2/2,
Γi(k,l)=I{czt[Ei(k,l)]}I[Ψi(p,q)δ(wwoi,ssoi)],
Mt(k,l)=χ(k,l)i=1FΓi(k,l).
Mt(k,l)=χ(k,l){i=1F[Ii(m,n)Φ0(m,n)]I{[Φi(u,v)Ψi(p,q)]δ(wwoi,ssoi)}}.
Ri(m,n)=[χ*(k,l)i=1FΓi*(k,l)χ(k,l)]I[ζ(w,s)hi(w,s)],

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