Abstract

We propose a new, to our knowledge, stream cipher technique for two-dimensional (2-D) image data that can be implemented by iterative optical transformation. The stream cipher uses a pseudorandom number generator (PRNG) to generate a pseudorandom bit sequence. The proposed method for the PRNG is composed of the iterative operation of 2-D affine transformation achieved by optical components and by modulo-n addition of the transformed images. We expect efficient execution of the method by optical parallel processing. We verify the performance of the proposed method in terms of security strength and clarify problems on optical implementation by the optical fractal synthesizer.

© 2000 Optical Society of America

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References

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  1. B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
    [CrossRef]
  2. P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef] [PubMed]
  3. B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
    [CrossRef]
  4. B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
    [CrossRef]
  5. B. Javidi, G. Zhang, J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054–1058 (1997).
    [CrossRef] [PubMed]
  6. G. Unnikrishnan, J. Joseph, K. Singh, “Optical encryption system that uses phase conjugation in a photorefractive crystal,” Appl. Opt. 37, 8181–8186 (1998).
    [CrossRef]
  7. O. Matoba, B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
    [CrossRef]
  8. M. Madjarova, M. Kakuta, M. Yamaguchi, N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
    [CrossRef]
  9. M. Kakuta, M. Madjarova, T. Obi, M. Yamaguchi, N. Ohyama, “Vernam encryption using optical parallel processing,” Jpn. J. Opt. 27, 104–109 (1998).
  10. S. Zhang, M. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).
    [CrossRef]
  11. J. Tanida, A. Uemoto, Y. Ichioka, “Optical fractal synthesizer: concept and experimental verification,” Appl. Opt. 32, 653–658 (1993).
    [CrossRef] [PubMed]
  12. J. L. Massey, “Shift-register synthesis and BCH decoding,” IEEE Trans. Inf. Theory IT-15, 122–127 (1969).
    [CrossRef]

1999

1998

M. Kakuta, M. Madjarova, T. Obi, M. Yamaguchi, N. Ohyama, “Vernam encryption using optical parallel processing,” Jpn. J. Opt. 27, 104–109 (1998).

G. Unnikrishnan, J. Joseph, K. Singh, “Optical encryption system that uses phase conjugation in a photorefractive crystal,” Appl. Opt. 37, 8181–8186 (1998).
[CrossRef]

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

1997

1996

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

1995

1994

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

1993

1969

J. L. Massey, “Shift-register synthesis and BCH decoding,” IEEE Trans. Inf. Theory IT-15, 122–127 (1969).
[CrossRef]

Ahouzi, E.

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Horner, J. L.

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Ichioka, Y.

Javidi, B.

O. Matoba, B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[CrossRef]

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

B. Javidi, G. Zhang, J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054–1058 (1997).
[CrossRef] [PubMed]

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

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

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Joseph, J.

Kakuta, M.

M. Kakuta, M. Madjarova, T. Obi, M. Yamaguchi, N. Ohyama, “Vernam encryption using optical parallel processing,” Jpn. J. Opt. 27, 104–109 (1998).

M. Madjarova, M. Kakuta, M. Yamaguchi, N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
[CrossRef]

Karim, M.

S. Zhang, M. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).
[CrossRef]

Li, J.

B. Javidi, G. Zhang, J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054–1058 (1997).
[CrossRef] [PubMed]

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Madjarova, M.

M. Kakuta, M. Madjarova, T. Obi, M. Yamaguchi, N. Ohyama, “Vernam encryption using optical parallel processing,” Jpn. J. Opt. 27, 104–109 (1998).

M. Madjarova, M. Kakuta, M. Yamaguchi, N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
[CrossRef]

Massey, J. L.

J. L. Massey, “Shift-register synthesis and BCH decoding,” IEEE Trans. Inf. Theory IT-15, 122–127 (1969).
[CrossRef]

Matoba, O.

Obi, T.

M. Kakuta, M. Madjarova, T. Obi, M. Yamaguchi, N. Ohyama, “Vernam encryption using optical parallel processing,” Jpn. J. Opt. 27, 104–109 (1998).

Ohyama, N.

M. Kakuta, M. Madjarova, T. Obi, M. Yamaguchi, N. Ohyama, “Vernam encryption using optical parallel processing,” Jpn. J. Opt. 27, 104–109 (1998).

M. Madjarova, M. Kakuta, M. Yamaguchi, N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
[CrossRef]

Réfrégier, P.

Sergent, A.

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Singh, K.

Tanida, J.

Uemoto, A.

Unnikrishnan, G.

Yamaguchi, M.

M. Kakuta, M. Madjarova, T. Obi, M. Yamaguchi, N. Ohyama, “Vernam encryption using optical parallel processing,” Jpn. J. Opt. 27, 104–109 (1998).

M. Madjarova, M. Kakuta, M. Yamaguchi, N. Ohyama, “Optical implementation of the stream cipher based on the irreversible cellular automata algorithm,” Opt. Lett. 22, 1624–1626 (1997).
[CrossRef]

Zhang, G.

B. Javidi, G. Zhang, J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054–1058 (1997).
[CrossRef] [PubMed]

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Zhang, S.

S. Zhang, M. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).
[CrossRef]

Appl. Opt.

IEEE Trans. Inf. Theory

J. L. Massey, “Shift-register synthesis and BCH decoding,” IEEE Trans. Inf. Theory IT-15, 122–127 (1969).
[CrossRef]

Jpn. J. Opt.

M. Kakuta, M. Madjarova, T. Obi, M. Yamaguchi, N. Ohyama, “Vernam encryption using optical parallel processing,” Jpn. J. Opt. 27, 104–109 (1998).

Opt. Eng.

S. Zhang, M. Karim, “High-security optical integrated stream ciphers,” Opt. Eng. 38, 20–24 (1999).
[CrossRef]

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

B. Javidi, G. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Opt. Lett.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of the proposed method: (a) encoding and (b) decoding methods, (c) PRNG.

Fig. 2
Fig. 2

Image sequence generated by the PRNG.

Fig. 3
Fig. 3

Patterns generated by different parameter sets of affine transformations.

Fig. 4
Fig. 4

Verification of the proposed method: (a) message, (b) key pattern, (c) encrypted message, (d) encoded message.

Fig. 5
Fig. 5

Decoded images by modified key pattern. Images correspond to information given in Table 3.

Fig. 6
Fig. 6

Schematic diagram of linear feedback shift register.

Fig. 7
Fig. 7

Trace of a bright pixel during iteration.

Fig. 8
Fig. 8

Autocorrelation function of the generated patterns.

Fig. 9
Fig. 9

Optical setup of optical fractal synthesizer. BS, beam splitter.

Fig. 10
Fig. 10

Random pattern sequence generated by the optical system.

Fig. 11
Fig. 11

Result of optical implementation: (a) message, (b) data encrypted by a key generated optically, (c) message decoded by a key pattern generated independently, (d) intensity difference between the keys used for (b) and (c), and (e) message decoded by the key pattern used for (b).

Tables (4)

Tables Icon

Table 1 Coefficients of Affine Transformations for Patterns of Figs. 3(a), 3(b), and 3(d)

Tables Icon

Table 2 Coefficients of Affine Transformations for Key Pattern of Fig. 4(b)

Tables Icon

Table 3 Modified Parameters and Variations of Fig. 5

Tables Icon

Table 4 Parameters of Affine Transformations Used in Optical Implementation

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

x=a bc dx+ef,
Rθ=cos θ -sin θsin θ cos θ,
Ss=s 00 s,
x=SsRθx+t,
sj=i=1mod 2Lcisj-1,
fj+1x=i=0mod nNfjAi-1x-ai,

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