Abstract

We have shown that the application of double random phase encoding (DRPE) to biometrics enables the use of biometrics as cipher keys for binary data encryption. However, DRPE is reported to be vulnerable to known-plaintext attacks (KPAs) using a phase recovery algorithm. In this study, we investigated the vulnerability of DRPE using fingerprints as cipher keys to the KPAs. By means of computational experiments, we estimated the encryption key and restored the fingerprint image using the estimated key. Further, we propose a method for avoiding the KPA on the DRPE that employs the phase retrieval algorithm. The proposed method makes the amplitude component of the encrypted image constant in order to prevent the amplitude component of the encrypted image from being used as a clue for phase retrieval. Computational experiments showed that the proposed method not only avoids revealing the cipher key and the fingerprint but also serves as a sufficiently accurate verification system.

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References

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    [CrossRef] [PubMed]
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2007 (1)

2006 (4)

2005 (1)

2004 (1)

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt . 33, 37–44 (2004) in Japanese.

2000 (1)

1998 (1)

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37(2), 565–569 (1998).
[CrossRef]

1995 (1)

1982 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Ahouzi, E.

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37(2), 565–569 (1998).
[CrossRef]

Arcos, S.

Carnicer, A.

Castro, A.

Chiou, A. E. T.

Fienup, J. R.

Frauel, Y.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Gopinathan, U.

Javidi, B.

Juvells, I.

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Obi, T.

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14(5), 1755–1766 (2006).
[CrossRef] [PubMed]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt . 33, 37–44 (2004) in Japanese.

Ohyama, N.

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14(5), 1755–1766 (2006).
[CrossRef] [PubMed]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt . 33, 37–44 (2004) in Japanese.

Peng, X.

Refregier, P.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Sergent, A.

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37(2), 565–569 (1998).
[CrossRef]

Sheridan, J. T.

Su, W.-C.

Sun, C.-C.

Suzuki, H.

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14(5), 1755–1766 (2006).
[CrossRef] [PubMed]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt . 33, 37–44 (2004) in Japanese.

Tashima, H.

Wang, B.

Wei, H.

Yachida, M.

Yamaguchi, M.

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14(5), 1755–1766 (2006).
[CrossRef] [PubMed]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt . 33, 37–44 (2004) in Japanese.

Yamaya, T.

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt . 33, 37–44 (2004) in Japanese.

Yu, B.

Zhang, P.

Appl. Opt. (2)

Jpn. J. Opt (1)

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt . 33, 37–44 (2004) in Japanese.

Opt. Eng. (1)

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37(2), 565–569 (1998).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Other (1)

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50

Supplementary Material (1)

» Media 1: AVI (2367 KB)     

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Figures (7)

Fig. 1
Fig. 1

Encryption by double random phase encoding

Fig. 2
Fig. 2

Decryption by double random phase encoding

Fig. 3
Fig. 3

Images in the encryption scheme: (a) plaintext image to be encrypted; (b) random phase image to be multiplied with (a); (c) fingerprint image; (d) phase image of Fourier transform of (c); (e) key image for encryption, which is the center part of (d); (f) restored fingerprint image, which is the inverse Fourier transform of (e); (g) amplitude component of the encrypted image; and (h) phase component of the encrypted image.

Fig. 4
Fig. 4

SSEs of the phase retrieval algorithm versus iteration (left) and POC peak between plaintext image and decrypted image of the encrypted image used in the KPA versus iteration (right).

Fig. 5
Fig. 5

Recovery accuracy versus iterations in the case of the restored fingerprint image (left) and in the case of the restored plain image that is obtained by decrypting another encrypted image with the estimated key (right).

Fig. 6
Fig. 6

(Media 1) Single frame excerpt from animation showing convergence of the KPA during the GS algorithm; images obtained after 215 iterations: (a)–(d) are for the conventional method and (e)–(h) are for the phase-only method. (a) and (e) show amplitude images obtained by the GS algorithm; (b) and (f) show revealed key images; (c) and (g) show images decrypted from another encrypted image; and (d) and (h) show fingerprint images, which are inverse Fourier transforms of (b) and (f), respectively.

Fig. 7
Fig. 7

Examples of decrypted images: (a) and (b) conventional method; (c) and (d) phase-only method; (a) and (c) using same individual’s fingerprint image; and (b) and (d) using different individual’s fingerprint image.

Tables (1)

Tables Icon

Table 1 Comparison of Bit Error Rate

Equations (10)

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f m ( x , y ) = f ( x , y ) exp { j r ( x , y ) } .
Φ ( u , v ) = F m ( u , v ) exp { j K E ( u , v ) } .
f ^ m ( x d , y d ) = [ F m * ( u , v ) N ( u , v ) ] = f m * ( x d , y d ) * n ( x d , y d ) ,
n ( x d , y d ) { δ ( x d α , y d β ) r a n d o m s e q u e n c e ( c o r r e c t ​ ​     f i n g e r p r i n t )         ( i n c o r r e c t     f i n g e r p r i n t ) ,
| Φ ( u , v ) | = | F m ( u , v ) |
exp { j K ^ E ( u , v ) } = Φ ( u , v ) F ^ m ( u , v ) = Φ ( u , v ) [ f ( x , y ) exp { j r ^ ( x , y ) } ] .
Φ p ( u , v ) = Φ ( u , v ) | Φ ( u , v ) | .
f ^ p ( x d , y d ) = [ F m * ( u , v ) | F m ( u , v ) | N ( u , v ) ] = f p ( x d , y d ) * n ( x d , y d ) ,
S S E = 10 log [ f | f m ( n ) | ] f 2 ,
B E R = N e r r o r N t o t a l ,

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