Abstract

This study employed the optical responses of periodic structures, multiple-variable functions with sufficient complexity, to develop a cryptographic scheme. The characteristics of structures could be delivered easily with the ciphertext, a series of numbers containing plaintext messages. Two optimization methods utilizing a genetic algorithm were adopted to generate the periodic structure profile as a critical encryption/decryption key. The robustness of methods was further confirmed under various limits. The ciphertext could only be decrypted by referring to the codebook after acquiring the pre-determined optical response. The confidentiality and large capacity of the scheme revealed the enhanced coding strategies here while the success of the scheme was demonstrated with the delivery of an example message.

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References

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2010 (2)

2008 (2)

R. Katayama and Y. Komatsu, “Blue/DVD/CD compatible optical head,” Appl. Opt. 47(22), 4045–4054 (2008).
[CrossRef] [PubMed]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, “Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared,” J. Comput. Theor. Nanosci. 5, 201–213 (2008).

2005 (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

2004 (2)

M. Zhou, S. D. Chang, and C. P. Grover, “Cryptography based on the absorption/emission features of multicolor semiconductor nanocrystal quantum dots,” Opt. Express 12(13), 2925–2931 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-13-2925 .
[CrossRef] [PubMed]

H. C. Cheng and Y. L. Lo, “Arbitrary strain distribution measurement using a genetic algorithm approach and two fiber Bragg grating intensity spectra,” Opt. Commun. 239(4-6), 323–332 (2004).
[CrossRef]

2003 (1)

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74(11), 4885–4892 (2003).
[CrossRef]

2002 (2)

N. Gisin, G. G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297(5589), 2026–2030 (2002).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

C. T. Clelland, V. Risca, and C. Bancroft, “Hiding messages in DNA microdots,” Nature 399(6736), 533–534 (1999).
[CrossRef] [PubMed]

1995 (2)

1981 (1)

1978 (1)

R. L. Rivest, A. Shamir, and L. Adleman, “Method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM 21(2), 120–126 (1978).
[CrossRef]

Abushagur, M. A. G.

Adleman, L.

R. L. Rivest, A. Shamir, and L. Adleman, “Method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM 21(2), 120–126 (1978).
[CrossRef]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Bancroft, C.

C. T. Clelland, V. Risca, and C. Bancroft, “Hiding messages in DNA microdots,” Nature 399(6736), 533–534 (1999).
[CrossRef] [PubMed]

Chang, S. D.

Chen, J. S.

Chen, W.

Chen, X. D.

Chen, Y.-B.

Y.-B. Chen and J. S. Chen, “Cryptosystem for plaintext messages utilizing optical properties of gratings,” Appl. Opt. 49(11), 2041–2046 (2010).
[CrossRef] [PubMed]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, “Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared,” J. Comput. Theor. Nanosci. 5, 201–213 (2008).

Cheng, H. C.

H. C. Cheng and Y. L. Lo, “Arbitrary strain distribution measurement using a genetic algorithm approach and two fiber Bragg grating intensity spectra,” Opt. Commun. 239(4-6), 323–332 (2004).
[CrossRef]

Clelland, C. T.

C. T. Clelland, V. Risca, and C. Bancroft, “Hiding messages in DNA microdots,” Nature 399(6736), 533–534 (1999).
[CrossRef] [PubMed]

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Fischer, I.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Garcia-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Gaylord, T. K.

Gershenfeld, N.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297(5589), 2026–2030 (2002).
[CrossRef] [PubMed]

Gisin, N.

N. Gisin, G. G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Grover, C. P.

Javidi, B.

Johnson, E. G.

Katayama, R.

Komatsu, Y.

Larger, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Lee, B. J.

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, “Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared,” J. Comput. Theor. Nanosci. 5, 201–213 (2008).

Lo, Y. L.

H. C. Cheng and Y. L. Lo, “Arbitrary strain distribution measurement using a genetic algorithm approach and two fiber Bragg grating intensity spectra,” Opt. Commun. 239(4-6), 323–332 (2004).
[CrossRef]

Mirasso, C. R.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Moharam, M. G.

Nomura, T.

Pappu, R.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297(5589), 2026–2030 (2002).
[CrossRef] [PubMed]

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Recht, B.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297(5589), 2026–2030 (2002).
[CrossRef] [PubMed]

Refregier, P.

Ribordy, G. G.

N. Gisin, G. G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Risca, V.

C. T. Clelland, V. Risca, and C. Bancroft, “Hiding messages in DNA microdots,” Nature 399(6736), 533–534 (1999).
[CrossRef] [PubMed]

Rivest, R. L.

R. L. Rivest, A. Shamir, and L. Adleman, “Method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM 21(2), 120–126 (1978).
[CrossRef]

Shamir, A.

R. L. Rivest, A. Shamir, and L. Adleman, “Method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM 21(2), 120–126 (1978).
[CrossRef]

Shen, Y. J.

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74(11), 4885–4892 (2003).
[CrossRef]

Sheppard, C. J. R.

Shore, K. A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Taylor, J.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297(5589), 2026–2030 (2002).
[CrossRef] [PubMed]

Tittel, W.

N. Gisin, G. G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Zbinden, H.

N. Gisin, G. G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Zhang, Z. M.

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, “Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared,” J. Comput. Theor. Nanosci. 5, 201–213 (2008).

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74(11), 4885–4892 (2003).
[CrossRef]

Zhou, M.

Zhu, Q. Z.

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74(11), 4885–4892 (2003).
[CrossRef]

Appl. Opt. (2)

Commun. ACM (1)

R. L. Rivest, A. Shamir, and L. Adleman, “Method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM 21(2), 120–126 (1978).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, “Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared,” J. Comput. Theor. Nanosci. 5, 201–213 (2008).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nature (2)

C. T. Clelland, V. Risca, and C. Bancroft, “Hiding messages in DNA microdots,” Nature 399(6736), 533–534 (1999).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438 (7066), 343–346 (2005).
[CrossRef] [PubMed]

Opt. Commun. (1)

H. C. Cheng and Y. L. Lo, “Arbitrary strain distribution measurement using a genetic algorithm approach and two fiber Bragg grating intensity spectra,” Opt. Commun. 239(4-6), 323–332 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Rev. Mod. Phys. (1)

N. Gisin, G. G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[CrossRef]

Rev. Sci. Instrum. (1)

Y. J. Shen, Q. Z. Zhu, and Z. M. Zhang, “A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces,” Rev. Sci. Instrum. 74(11), 4885–4892 (2003).
[CrossRef]

Science (1)

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297(5589), 2026–2030 (2002).
[CrossRef] [PubMed]

Other (6)

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).

S. S. Rao, Engineering Optimization: Theory and Practice (John Wiley, 2009).

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (M. Dekker, 1997).

F. P. Incropera, D. P. DeWitt, T. L. Bergman, and A. S. Lavain, Fundamentals of Heat and Mass Transfer (John Wiley, 2007).

A. J. Menezes, P. C. Van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography (CRC Press, 1997).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

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Figures (6)

Fig. 1
Fig. 1

One-dimensional periodic structures at a plane wave incidence. The optical responses are employed within the proposed cryptographic scheme and the dimensions are determined by the groove depth d, lateral filling ratio f, and grating period Λ, respectively. S 1, S 2, and S 3 are the reflected intensity when the angle of incidence is θ1, θ2, and θ3, respectively.

Fig. 2
Fig. 2

(a) The flowchart of a typical GA algorithm used for optimization; (b) Equally-spaced grids constructed in the space for the three dimensional grid search method.

Fig. 3
Fig. 3

Working principles of the proposed cryptographic scheme are demonstrated using the characters “E” and “F.” (a) Encryption process; (b) Decryption process.

Fig. 4
Fig. 4

Satisfactory optical responses of suitable structures for the demonstration of the robustness of the optimization methods: (a) The directional reflectance from a Ag grating at the TM wave incidence; (b) The directional reflectance from a Ag grating at the TE wave incidence; (c) The directional reflectance from a Al grating at the TM wave incidence; (d) The directional transmittance through a Ag slit array at the TE wave incidence. The ideal values of optical responses are marked with red solid circles.

Fig. 5
Fig. 5

(a) The map of fitness function results at the beginning of the hybrid optimization method. (b) Efficiency comparison between the two optimization methods under the same constraints.

Fig. 6
Fig. 6

(a) An illustration of the proposed cryptographic system using a sample message “NANO.” Enhanced coding strategies are incorporated within ciphertext I and ciphertext II such that the message can be sent securely and easily. (b) The directional reflectance spectra from the Ag grating employed in the illustration. The Key_1 can be a single or multiple number of incident wavelength. The Key_2 is the structural dimensions found in Fig. 4(a) and the Key_3 is a codebook shown in Fig. 3(a).

Equations (5)

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ε ( ω ) = ε ω p 2 ω 2 + i ω γ
u 1 = α u 1 + ( 1 α ) u 2
u 2 = ( 1 α ) u 1 + α u 2
E = i = 1 3 ( R ideal, i R i ) 2
sin θ j = sin θ + j λ Λ

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