Abstract

In this work, we evaluate the avalanche effect and bit independence properties of the double random phase encoding (DRPE) algorithm in the Fourier and Fresnel domains. Experimental results show that DRPE has excellent bit independence characteristics in both the Fourier and Fresnel domains. However, DRPE achieves better avalanche effect results in the Fresnel domain than in the Fourier domain. DRPE gives especially poor avalanche effect results in the Fourier domain when only one bit is changed in the plaintext or in the encryption key. Despite this, DRPE shows satisfactory avalanche effect results in the Fresnel domain when any other number of bits changes in the plaintext or in the encryption key. To the best of our knowledge, this is the first report on the avalanche effect and bit independence behaviors of optical encryption approaches for bit units.

© 2014 Optical Society of America

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References

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2013

2011

2010

2009

2008

2007

2006

J. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532–536 (2006).
[CrossRef]

2005

2004

2003

2001

2000

1999

1998

1995

1973

H. Feistel, “Cryptography and computer privacy,” Sci. Am. 228, 15–23 (1973).
[CrossRef]

Alam, M.

Alfalou, A.

Arcos, S.

Barrera, J.

J. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532–536 (2006).
[CrossRef]

Blondeau, C.

C. Blondeau and K. Nyberg, “New links between differential and linear cryptanalysis,” Lect. Notes Comput. Sci. 7881, 388–404 (2013).
[CrossRef]

Bollaro, F.

Bolognini, N.

J. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532–536 (2006).
[CrossRef]

Carnicer, A.

Castro, A.

Chen, W.

Chen, X.

Cho, M.

Clemente, P.

Dowling, T.

Durán, V.

Feistel, H.

H. Feistel, “Cryptography and computer privacy,” Sci. Am. 228, 15–23 (1973).
[CrossRef]

Frauel, Y.

Gopinathan, U.

Goudail, F.

Hara, M.

M. Toishi, M. Hara, K. Tanaka, T. Tanaka, and K. Watanabe, “Novel encryption method using multi reference patterns in coaxial holographic data storage,” Jpn. J. Appl. Phys. 46, 3775 (2007).
[CrossRef]

Hayasaki, Y.

Henao, R.

J. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532–536 (2006).
[CrossRef]

Hennelly, B.

Ide, M.

Javidi, B.

Joseph, J.

Juvells, I.

Kim, D.

Kim, H.

Kishk, S.

Kumar, A.

Kumar, P.

Kuroda, K.

Lancis, J.

Lee, Y.

Liu, H.

Luo, Z.

Mansour, A.

Matoba, O.

Matsuba, Y.

Millan, M.

O. Matoba, T. Nomura, E. Pérez-Cabré, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Monaghan, D.

Montes-Usategui, M.

Nagaoka, A.

Naughton, T.

Nishida, N.

Nomura, T.

O. Matoba, T. Nomura, E. Pérez-Cabré, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Nyberg, K.

C. Blondeau and K. Nyberg, “New links between differential and linear cryptanalysis,” Lect. Notes Comput. Sci. 7881, 388–404 (2013).
[CrossRef]

Obi, T.

Okada-Shudo, Y.

Pérez-Cabré, E.

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Réfrégier, P.

Sheng, Y.

Sheppard, C.

Sheridan, J.

Shimura, T.

Singh, K.

Stallings, W.

W. Stallings, Cryptography and Network Security Principles and Practice (Prentice Hall, 2011).

Suzuki, H.

Tajahuerce, E.

Takeda, M.

Tan, X.

Tanaka, K.

M. Toishi, M. Hara, K. Tanaka, T. Tanaka, and K. Watanabe, “Novel encryption method using multi reference patterns in coaxial holographic data storage,” Jpn. J. Appl. Phys. 46, 3775 (2007).
[CrossRef]

Tanaka, T.

M. Toishi, M. Hara, K. Tanaka, T. Tanaka, and K. Watanabe, “Novel encryption method using multi reference patterns in coaxial holographic data storage,” Jpn. J. Appl. Phys. 46, 3775 (2007).
[CrossRef]

Tashima, H.

Tebaldi, M.

J. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532–536 (2006).
[CrossRef]

Toishi, M.

M. Toishi, M. Hara, K. Tanaka, T. Tanaka, and K. Watanabe, “Novel encryption method using multi reference patterns in coaxial holographic data storage,” Jpn. J. Appl. Phys. 46, 3775 (2007).
[CrossRef]

Torres-Company, V.

Torroba, R.

J. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532–536 (2006).
[CrossRef]

Towghi, N.

Unnikrishnan, G.

Watanabe, K.

M. Toishi, M. Hara, K. Tanaka, T. Tanaka, and K. Watanabe, “Novel encryption method using multi reference patterns in coaxial holographic data storage,” Jpn. J. Appl. Phys. 46, 3775 (2007).
[CrossRef]

Wen, W.

Xiao, D.

Xiao-Feng, L.

Xin, L.

Xin, Z.

Yamamoto, H.

Zhang, Y.

Appl. Opt.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

M. Toishi, M. Hara, K. Tanaka, T. Tanaka, and K. Watanabe, “Novel encryption method using multi reference patterns in coaxial holographic data storage,” Jpn. J. Appl. Phys. 46, 3775 (2007).
[CrossRef]

Lect. Notes Comput. Sci.

C. Blondeau and K. Nyberg, “New links between differential and linear cryptanalysis,” Lect. Notes Comput. Sci. 7881, 388–404 (2013).
[CrossRef]

Opt. Commun.

J. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption-decryption via lateral shifting of a random phase mask,” Opt. Commun. 259, 532–536 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35, 2391–2393 (2010).
[CrossRef]

W. Chen, X. Chen, and C. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[CrossRef]

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

Y. Zhang, D. Xiao, W. Wen, and H. Liu, “Vulnerability to chosen-plaintext attack of a general optical encryption model with the architecture of scrambling-then-double random phase encoding,” Opt. Lett. 38, 4506–4509 (2013).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
[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]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. 34, 331–333 (2009).
[CrossRef]

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

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

Proc. IEEE

O. Matoba, T. Nomura, E. Pérez-Cabré, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Sci. Am.

H. Feistel, “Cryptography and computer privacy,” Sci. Am. 228, 15–23 (1973).
[CrossRef]

Other

W. Stallings, Cryptography and Network Security Principles and Practice (Prentice Hall, 2011).

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Figures (10)

Fig. 1.
Fig. 1.

(a) Schematic diagram of DRPE system in the Fourier domain. (b) Schematic diagram of DRPE system in the Fresnel domain.

Fig. 2.
Fig. 2.

Illustration of avalanche effect in data encryption (when a plaintext or key is changed slightly, the ciphertext changes significantly).

Fig. 3.
Fig. 3.

(a) Illustration of used grayscale image and (b) IEEE 754 double-precision binary floating-point format.

Fig. 4.
Fig. 4.

Avalanche effect with some bits in the plaintext inverted (Bit unit, compare the encrypted image with binary term. Pixel unit, compare the encrypted image with pixel values).

Fig. 5.
Fig. 5.

Avalanche effect with some bits in the phase keys inverted. (a) Avalanche effect with bits changed in the first phase key. (b) Avalanche effect with bits changed in the second phase key.

Fig. 6.
Fig. 6.

Avalanche effect with some bits in the wavelength and two distance values inverted.

Fig. 7.
Fig. 7.

(a) Illustration of used binary image. (b) Avalanche effect with some bits in the plaintext inverted for input binary image.

Fig. 8.
Fig. 8.

Avalanche effect with some bits in the phase keys inverted for input binary image. (a) Avalanche effect with bits changed in the first phase key. (b) Avalanche effect with bits changed in the second phase key.

Fig. 9.
Fig. 9.

Avalanche effect with some bits in the wavelength and two distance values inverted for input binary image.

Fig. 10.
Fig. 10.

Avalanche effect with some bits in the plaintext and two phase keys inverted for the photon-counting encryption method in [17] with input grayscale image.

Tables (9)

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Table 1. Avalanche Effect for DRPE in the Fourier and Fresnel Domains

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Table 2. Avalanche Effect for DRPE in the Fourier and Fresnel Domains

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Table 3. Avalanche Effect for DRPE in the Fresnel Domains

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Table 4. Bit Independence Criterion for DRPE in the Fourier and Fresnel Domains

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Table 5. Avalanche Effect for DRPE in the Fourier and Fresnel Domains for Input Binary Image

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Table 6. Avalanche Effect for DRPE in the Fourier and Fresnel Domains for Input Binary Image

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Table 7. Avalanche Effect for DRPE in the Fresnel Domains for Input Binary Image

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Table 8. Bit Independence Criterion for DRPE in the Fourier and Fresnel Domains for Binary Input Image

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Table 9. Avalanche Effect for Photon-Counting Encryption Method in [17]

Equations (5)

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f e ( x , y ) = I 1 [ I [ f ( x , y ) exp ( j 2 π n ( x , y ) ) ] exp [ j 2 π b ( μ , ν ) ] ] ,
g ( x , y ) = F r T λ { F r T λ { f ( x , y ) exp [ j ϕ ( x , y ) ] ; z 1 } exp [ j ψ ( x , y ) ] ; z 2 } ,
avalanche = H ( Y , Y ) Num ( Y ) or avalanche = H ( Y , Y ) Num ( Y ) ,
BI ( C ( b j ) , C ( b k ) ) = | corr ( ( b j 1 b j i b j N ) , ( b k 1 b k i b k N ) ) | ,
BIC ( E ( X , K ) ) = max 1 j , k N j k BI ( C ( b j ) , C ( b k ) ) ,

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