Abstract

A novel optical cryptosystem based on phase-truncated Fresnel diffraction (PTFD) and transport of intensity equation (TIE) is proposed. By using the phase truncation technique, a phase-encoded plaintext could be encrypted into a real-valued noise-like intensity distribution by employing a random amplitude mask (RAM) and a random phase mask (RPM), which are regarded as two secret keys. For decryption, a generalized amplitude-phase retrieval (GAPR) algorithm combined with the TIE method are proposed to recover the plaintext with the help of two keys. Different from the current phase-truncated-based optical cryptosystems which need record the truncated phase as decryption keys, our scheme do not need the truncated phase because of the introducing of the TIE method. Moreover, the proposed scheme is expected to against existing attacks. A set of numerical simulation results show the feasibility and security of the proposed method.

© 2015 Optical Society of America

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References

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2013 (7)

2012 (2)

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

X. Wang and D. Zhao, “Double images encryption method with resistance against the specific attack based on an asymmetric algorithm,” Opt. Express 20(11), 11994–12003 (2012), doi:.
[Crossref] [PubMed]

2011 (2)

W. Qin, X. Peng, and X. Meng, “Cryptanalysis of optical encryption schemes based on joint transform correlator architecture,” Opt. Eng. 50(2), 028201(2011).
[Crossref]

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50(8), 080501 (2011).
[Crossref] [PubMed]

2010 (4)

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010).
[Crossref] [PubMed]

J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. 35(21), 3553–3555 (2010).
[Crossref] [PubMed]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283(20), 3917–3921 (2010).
[Crossref]

W. He, X. Peng, W. Qin, and X. Meng, “The keyed optical Hash function based on cascaded phase-truncated Fourier transforms,” Opt. Commun. 283(11), 2328–2332 (2010).
[Crossref]

2007 (1)

2006 (2)

2005 (1)

2001 (1)

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1–4), 65–75 (2001).
[Crossref]

2000 (1)

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39(8), 2031–2035 (2000).
[Crossref]

1997 (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

1995 (1)

1983 (1)

1982 (1)

Allen, L. J.

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1–4), 65–75 (2001).
[Crossref]

Arcos, S.

Asundi, A.

Barrera, J. F.

J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. 35(21), 3553–3555 (2010).
[Crossref] [PubMed]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283(20), 3917–3921 (2010).
[Crossref]

Bolognini, N.

Carnicer, A.

Castro, A.

Chen, Q.

Chen, W.

Chen, X.

Chen, Y.

Dai, C.

Fienup, J. R.

Frauel, Y.

Gao, B.

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50(8), 080501 (2011).
[Crossref] [PubMed]

Gopinathan, U.

He, W.

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm: comment,” Opt. Lett. 38(20), 4044(2013).
[Crossref] [PubMed]

M. Liao, W. He, X. Peng, X. Liu, and X. Meng, “Cryptanalysis of optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Laser Technol. 45, 763–767 (2013).
[Crossref]

C. Zhang, M. Liao, W. He, and X. Peng, “Ciphertext-only attack on a joint transform correlator encryption system,” Opt. Express 21(23), 28523–28530 (2013).
[Crossref] [PubMed]

W. He, X. Peng, W. Qin, and X. Meng, “The keyed optical Hash function based on cascaded phase-truncated Fourier transforms,” Opt. Commun. 283(11), 2328–2332 (2010).
[Crossref]

Javidi, B.

Juvells, I.

Liao, M.

M. Liao, W. He, X. Peng, X. Liu, and X. Meng, “Cryptanalysis of optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Laser Technol. 45, 763–767 (2013).
[Crossref]

C. Zhang, M. Liao, W. He, and X. Peng, “Ciphertext-only attack on a joint transform correlator encryption system,” Opt. Express 21(23), 28523–28530 (2013).
[Crossref] [PubMed]

Liu, S.

Liu, W.

Liu, X.

M. Liao, W. He, X. Peng, X. Liu, and X. Meng, “Cryptanalysis of optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Laser Technol. 45, 763–767 (2013).
[Crossref]

Liu, Z.

Meng, X.

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm: comment,” Opt. Lett. 38(20), 4044(2013).
[Crossref] [PubMed]

M. Liao, W. He, X. Peng, X. Liu, and X. Meng, “Cryptanalysis of optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Laser Technol. 45, 763–767 (2013).
[Crossref]

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50(8), 080501 (2011).
[Crossref] [PubMed]

W. Qin, X. Peng, and X. Meng, “Cryptanalysis of optical encryption schemes based on joint transform correlator architecture,” Opt. Eng. 50(2), 028201(2011).
[Crossref]

W. He, X. Peng, W. Qin, and X. Meng, “The keyed optical Hash function based on cascaded phase-truncated Fourier transforms,” Opt. Commun. 283(11), 2328–2332 (2010).
[Crossref]

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Nomura, T.

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39(8), 2031–2035 (2000).
[Crossref]

Oxley, M. P.

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1–4), 65–75 (2001).
[Crossref]

Peng, X.

M. Liao, W. He, X. Peng, X. Liu, and X. Meng, “Cryptanalysis of optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Laser Technol. 45, 763–767 (2013).
[Crossref]

W. He, X. Meng, and X. Peng, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm: comment,” Opt. Lett. 38(20), 4044(2013).
[Crossref] [PubMed]

C. Zhang, M. Liao, W. He, and X. Peng, “Ciphertext-only attack on a joint transform correlator encryption system,” Opt. Express 21(23), 28523–28530 (2013).
[Crossref] [PubMed]

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50(8), 080501 (2011).
[Crossref] [PubMed]

W. Qin, X. Peng, and X. Meng, “Cryptanalysis of optical encryption schemes based on joint transform correlator architecture,” Opt. Eng. 50(2), 028201(2011).
[Crossref]

W. He, X. Peng, W. Qin, and X. Meng, “The keyed optical Hash function based on cascaded phase-truncated Fourier transforms,” Opt. Commun. 283(11), 2328–2332 (2010).
[Crossref]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010).
[Crossref] [PubMed]

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

Qin, W.

W. Qin, X. Peng, and X. Meng, “Cryptanalysis of optical encryption schemes based on joint transform correlator architecture,” Opt. Eng. 50(2), 028201(2011).
[Crossref]

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50(8), 080501 (2011).
[Crossref] [PubMed]

W. He, X. Peng, W. Qin, and X. Meng, “The keyed optical Hash function based on cascaded phase-truncated Fourier transforms,” Opt. Commun. 283(11), 2328–2332 (2010).
[Crossref]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010).
[Crossref] [PubMed]

Qu, W.

Reed Teague, M.

Refregier, P.

Sheridan, J. T.

Tebaldi, M.

J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. 35(21), 3553–3555 (2010).
[Crossref] [PubMed]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283(20), 3917–3921 (2010).
[Crossref]

Torroba, R.

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283(20), 3917–3921 (2010).
[Crossref]

J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. 35(21), 3553–3555 (2010).
[Crossref] [PubMed]

Vargas, C.

J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. 35(21), 3553–3555 (2010).
[Crossref] [PubMed]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283(20), 3917–3921 (2010).
[Crossref]

Wang, X.

Wei, H.

Yu, B.

Yu, Y.

Zhang, C.

Zhang, P.

Zhao, D.

Zuo, C.

Adv. Opt. Photon. (1)

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Opt. Commun. (4)

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1–4), 65–75 (2001).
[Crossref]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

W. He, X. Peng, W. Qin, and X. Meng, “The keyed optical Hash function based on cascaded phase-truncated Fourier transforms,” Opt. Commun. 283(11), 2328–2332 (2010).
[Crossref]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283(20), 3917–3921 (2010).
[Crossref]

Opt. Eng. (3)

W. Qin, X. Peng, and X. Meng, “Cryptanalysis of optical encryption schemes based on joint transform correlator architecture,” Opt. Eng. 50(2), 028201(2011).
[Crossref]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39(8), 2031–2035 (2000).
[Crossref]

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50(8), 080501 (2011).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Laser Technol. (1)

M. Liao, W. He, X. Peng, X. Liu, and X. Meng, “Cryptanalysis of optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Laser Technol. 45, 763–767 (2013).
[Crossref]

Opt. Lett. (7)

Phys. Today (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005), Chap. 3.

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Figures (8)

Fig. 1
Fig. 1 The flow chart of the encryption process. PTFD: phase-truncated Fresnel diffraction; E: ciphertext.
Fig. 2
Fig. 2 Sketch of optical setup for PTFD. SLM: space-light modulator; PC: personal computer.
Fig. 3
Fig. 3 The flow chart of the decryption process. GAPR: generalized amplitude-phase retrieval algorithm; TIE: transport of intensity equation.
Fig. 4
Fig. 4 The flow chart of the GAPR algorithm. FD and IFD denote Fresnel diffraction and inverse Fresnel diffraction, respectively.
Fig. 5
Fig. 5 (a) The CC values between the original plaintext and the recovered results using the TIE method, it declines while the diffraction distance d z 1 increases, (b) fix the diffraction distance d z 1 =10μm , the CC values between the original plaintext and the decrypted results using the MAPR and TIE methods, it also declines while the diffraction distance d z 2 increases.
Fig. 6
Fig. 6 The simulation results. (a) Original plaintext ‘Lena’, (b) ciphertext corresponding to (a), (c) decrypted result using the GAPR and TIE methods. The CC value between the decrypted image (c) and the plaintext (a) is 0.9501. (d) Original plaintext ‘Treasure map’, (e) ciphertext corresponding to (d), (f) decrypted result using the GAPR and TIE methods. The CC value between the decrypted image (f) and the plaintext (d) is 0.9936.
Fig. 7
Fig. 7 The flow chart of the phase retrieval process. GAPR: generalized amplitude-phase retrieval algorithm. The red parts are not available to the attackers.
Fig. 8
Fig. 8 The decrypted results using fake keys. (a) Decrypted result using a fake RPM and a fake RAM; (b) decrypted result using the true RPM and a fake RAM; (c) decrypted result using a fake RPM and the true RAM.

Equations (18)

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

u 0 (x,y)= R 1 (x,y)exp[ i2πf(x,y) ]
u 1 (x,y)=IFT{ FT[ u 0 (x,y) ] H 1 ( q x , q y ) } =IFT{ FT[ u 0 (x,y) ]exp[ ikd z 1 1 (λ q x ) 2 (λ q y ) 2 ] }
I 1 (x,y)= | u 1 (x,y) | 2
u 2 (x,y)=| u 1 (x,y) |exp[ i2π R 2 (x,y) ]
E(x,y)= | u 3 (x,y) | 2 = | IFT{ FT[ u 2 (x,y) ] H 2 ( q x , q y ) } | 2 = | IFT{ FT[ u 2 (x,y) ]exp[ ikd z 2 1 (λ q x ) 2 (λ q y ) 2 ] } | 2
G k (x,y)= E(x,y) exp[i Φ k (x,y)] g k (x,y)=IFD[ G k (x,y) ]= I k (x,y) exp[i φ k (x,y)] g k+1 (x,y)= I k (x,y) exp[i2π R 2 (x,y)] G k+1 (x,y)=FD[ g k+1 (x,y) ]=| G k+1 (x,y) |exp[i Φ k+1 (x,y)]
(i z + 2 2k +k) u 0 (x,y)=0
I 0 (x,y)= | u 0 (x,y) | 2
u 0 (x,y)= [ I 0 (x,y) ] 1/2 exp[ iφ(x,y) ]= R 1 (x,y)exp[ i2πf(x,y) ]
k I 0 (x,y) z =[ I 0 (x,y)φ(x,y) ]
ψ(x,y)= I 0 (x,y)φ(x,y)
2 ψ(x,y)=k I 0 (x,y) z
FT[ x (n) w(x,y) ]= i n q x n FT[ w(x,y) ]
ψ(x,y)=IFT[ ( q x 2 + q y 2 ) 1 FT( k I 0 (x,y) z ) ]
I 0 (x,y) z I (x,y) | R 1 (x,y) | 2 d z 1
φ(x,y)=IFT{ ( q x 2 + q y 2 ) 1 FT{ [ ψ(x,y) / I 0 (x,y) ] } }
f(x,y)= φ(x,y) / 2π
CC= m n ( A mn A ¯ )( B mn B ¯ ) ( m n ( A mn A ¯ ) 2 )( m n ( B mn B ¯ ) 2 )

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