Abstract

A hybrid optical scheme for efficient hardware implementation of the one-dimensional, three-neighborhood binary cellular automata rule ai=ai-1 XOR ai OR ai+1–based stream cipher is proposed. The system makes full use of the parallel, space-invariant, cascadable, and modular structure of the algorithm and is simple, robust, and compact. The number of cellular automata arrays can be as large as the number of pixels on the spatial light modulator, which results in an increase in speed (number of bits operated in parallel) and security (key length). The system can be made fully optical with the use of an optically addressable spatial light modulator for the input plane and for the nonlinear threshold element.

© 1997 Optical Society of America

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References

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1997 (2)

J.-W. Han, Y.-G. Taejon, and E.-S. Kim, Proc. SPIE 3073, 383 (1997).
[CrossRef]

B. Javidi, Phys. Today 50(3), 27 (1997).
[CrossRef]

1996 (2)

J. Horner and B. Javidi, eds., special issue on optical security, Opt. Eng. 35, 2451–2547 (1996).
[CrossRef]

H. Hinton, IEEE J. Sel. Topics Quantum Electron. 2, 14 (1996).
[CrossRef]

1995 (1)

N. S. Patel, K. L. Hall, and K. A. Bauschenbach, Proc. SPIE 2613, 126 (1995).
[CrossRef]

1994 (1)

1993 (2)

1991 (1)

S. Fukushima, T. Kurokawa, and Y. Sakai, IEEE Photon. Technol. Lett. 3, 1133 (1991).
[CrossRef]

1988 (1)

1987 (1)

1986 (2)

S. Wolfram, Adv. Appl. Math. 7, 123 (1986).
[CrossRef]

T. Yatagai, Appl. Opt. 25, 1571 (1986).
[CrossRef]

1985 (1)

1984 (1)

A. Sawchuk and T. Strand, Proc. IEEE,  72, 758 (1984).
[CrossRef]

Bauschenbach, K. A.

N. S. Patel, K. L. Hall, and K. A. Bauschenbach, Proc. SPIE 2613, 126 (1995).
[CrossRef]

Chavel, P.

Devos, F.

Fukushima, S.

S. Fukushima, T. Kurokawa, and Y. Sakai, IEEE Photon. Technol. Lett. 3, 1133 (1991).
[CrossRef]

Garda, P.

Glaser, I.

Hall, K. L.

N. S. Patel, K. L. Hall, and K. A. Bauschenbach, Proc. SPIE 2613, 126 (1995).
[CrossRef]

Han, J.-W.

J.-W. Han, Y.-G. Taejon, and E.-S. Kim, Proc. SPIE 3073, 383 (1997).
[CrossRef]

Hinton, H.

H. Hinton, IEEE J. Sel. Topics Quantum Electron. 2, 14 (1996).
[CrossRef]

Huang, K.

Ichioka, Y.

Ishikawa, M.

Javidi, B.

B. Javidi, Phys. Today 50(3), 27 (1997).
[CrossRef]

Jenkins, B.

Kim, E.-S.

J.-W. Han, Y.-G. Taejon, and E.-S. Kim, Proc. SPIE 3073, 383 (1997).
[CrossRef]

Kirk, A.

Kurokawa, T.

S. Fukushima, T. Kurokawa, and Y. Sakai, IEEE Photon. Technol. Lett. 3, 1133 (1991).
[CrossRef]

Li, G.

Y. Yin, G. Li, X. Yan, and L. Liu, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996) p. 296.

Liu, L.

Y. Yin, G. Li, X. Yan, and L. Liu, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996) p. 296.

Meier, W.

W. Meier and O. Staffelbach, in Advances in Cryptology—EUROCRYPT '91 (Springer-Verlag, Berlin, 1991), pp. 186–199.

Murdocca, M.

Patel, N. S.

N. S. Patel, K. L. Hall, and K. A. Bauschenbach, Proc. SPIE 2613, 126 (1995).
[CrossRef]

Sakai, Y.

S. Fukushima, T. Kurokawa, and Y. Sakai, IEEE Photon. Technol. Lett. 3, 1133 (1991).
[CrossRef]

Sawchuk, A.

Schneier, B.

B. Schneier, Applied Cryptography Protocols, Algorithms and Source Code in C, 2nd ed. (Wiley, New York, 1996), Chap. 16, p. 369.

Staffelbach, O.

W. Meier and O. Staffelbach, in Advances in Cryptology—EUROCRYPT '91 (Springer-Verlag, Berlin, 1991), pp. 186–199.

Strand, T.

A. Sawchuk and T. Strand, Proc. IEEE,  72, 758 (1984).
[CrossRef]

Tabata, T.

Tabory, J.

Taejon, Y.-G.

J.-W. Han, Y.-G. Taejon, and E.-S. Kim, Proc. SPIE 3073, 383 (1997).
[CrossRef]

Tanida, J.

Tooley, F.

Wakelin, S.

Wang, J.-M

Weber, A.

Wolfram, S.

S. Wolfram, Adv. Appl. Math. 7, 123 (1986).
[CrossRef]

Yan, X.

Y. Yin, G. Li, X. Yan, and L. Liu, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996) p. 296.

Yang, J.

Yatagai, T.

Yin, Y.

Y. Yin, G. Li, X. Yan, and L. Liu, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996) p. 296.

Adv. Appl. Math. (1)

S. Wolfram, Adv. Appl. Math. 7, 123 (1986).
[CrossRef]

Appl. Opt. (6)

IEEE J. Sel. Topics Quantum Electron. (1)

H. Hinton, IEEE J. Sel. Topics Quantum Electron. 2, 14 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Fukushima, T. Kurokawa, and Y. Sakai, IEEE Photon. Technol. Lett. 3, 1133 (1991).
[CrossRef]

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

Opt. Eng. (1)

J. Horner and B. Javidi, eds., special issue on optical security, Opt. Eng. 35, 2451–2547 (1996).
[CrossRef]

Phys. Today (1)

B. Javidi, Phys. Today 50(3), 27 (1997).
[CrossRef]

Proc. IEEE (1)

A. Sawchuk and T. Strand, Proc. IEEE,  72, 758 (1984).
[CrossRef]

Proc. SPIE (2)

N. S. Patel, K. L. Hall, and K. A. Bauschenbach, Proc. SPIE 2613, 126 (1995).
[CrossRef]

J.-W. Han, Y.-G. Taejon, and E.-S. Kim, Proc. SPIE 3073, 383 (1997).
[CrossRef]

Other (3)

B. Schneier, Applied Cryptography Protocols, Algorithms and Source Code in C, 2nd ed. (Wiley, New York, 1996), Chap. 16, p. 369.

W. Meier and O. Staffelbach, in Advances in Cryptology—EUROCRYPT '91 (Springer-Verlag, Berlin, 1991), pp. 186–199.

Y. Yin, G. Li, X. Yan, and L. Liu, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996) p. 296.

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Figures (4)

Fig. 1
Fig. 1

Block-schematic of the optical stream cipher based on a rule (1) one-dimensional (1-D) CA and the add-and-threshold method.

Fig. 2
Fig. 2

Experimental setup for a PRNG based on rule (1). BS's, beam splitters.

Fig. 3
Fig. 3

(a) Key pattern; (b) pattern after one round of 1024-cell CA, rule (1); (c) experimental pattern of (b) with the add-and-threshold method.

Fig. 4
Fig. 4

Computer simulation results of image encryption with the one-dimensional 1024-cell CA rule (1)–based stream cipher. The PRNG sequence is generated by sampling of 8  CA cells.

Equations (1)

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ai=ai-1 XOR ai OR ai+1.

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