Abstract

Novel information hiding for digital images based on binary encoding methods and pixel scrambling techniques is presented. First, a pixel scrambling technique is used to rearrange the pixels of a covert image to form a scrambled matrix by using a specified scrambling rule. Then, the gray values of all the pixels in the scrambled matrix are sequentially transformed into many sets of eight-digit binary codes. Subsequently, the eight-digit binary codes are encoded into a host image to form an overt image by using a specific encoding rule. Besides the eight-digit binary codes (information codes), the overt image contains five other groups of binary codes (specification codes), i.e., identification codes, gray-level codes, dimension codes, scrambling number codes, and scrambling time codes, to denote the parameters used for scrambling and encoding. According to the test results, the proposed method performs well. Moreover, the overt image and the host image look almost the same, and the decoded covert image is exactly the same as the original covert image.

© 2010 Optical Society of America

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References

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  1. Y. L. Yang, N. Cai, and G. Q. Ni, “Digital image scrambling technology based on the symmetry of Arnold transform,” J. Beijing Inst. Technol. 15, 216-220 (2006).
  2. B. Li and J. W. Xu, “Period of Arnold transformation and its application in image scrambling,” J. Cent. South Univ. Technol. 12, 278-282 (2005).
  3. T. Kong and D. Zhang, “A new anti-Arnold transformation algorithm,” J. Software 15, 1558-1564 (2004).
  4. D. Qi, J. Zou, and X. Han, “A new class of scrambling transformation and its application in the image information covering,” Sci. China Ser. E Technol. Sci. 43, 304-312 (2000).
  5. Y. Zhou, S. Agaian, V. M. Joyner, and K. Panetta, “Two Fibonacci p-code based image scrambling algorithms,” Proc. SPIE 6812, 681215 (2008).
  6. O. Lafe, “Data compression and encryption using cellular automata transforms,” Eng. Applic. Artif. Intell. 10, 581-591(1997).
  7. G. Z. Hernández and H. J. Herrmann, “Cellular automata for elementary image enhancement,” Graphical Models Image Process. 58, 82-89 (1996).
  8. C. C. Chang and J. C. Chuang, “An image intellectual property protection scheme for gray-level images using visual secret sharing strategy,” Pattern Recognit. Lett. 23, 931-941 (2002).
    [CrossRef]
  9. H. Zhang, J. Huang, and Z. Li, “New method of digital image scrambling based on binary tree generated by chaotic sequences,” Proc. SPIE 6790, 67905D (2007).
  10. R. Ye and H. Li, “A novel image scrambling and watermarking scheme based on cellular automata,” in 2008 International Symposium on Electronic Commerce and Security (2008), pp. 938-941.
  11. B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fraction Fourier domains,” Opt. Lett. 28, 269-271 (2003).
    [CrossRef]
  12. J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493-499(2005).
    [CrossRef]
  13. J. Zhao, H. Lu, and Q. Fan, “Color image encryption based on fractional Fourier transforms and pixel scrambling technique,” Proc. SPIE 6279, 62793B (2007).
  14. X. F. Meng, L. Z. Cai, X. L. Yang, X. X. Shen, and G. Y. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45, 3289 (2006).
    [CrossRef]
  15. Y. Y. Wang, Y. R. Wang, Y. Wang, H. J. Li, and W. J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761-765 (2007).
    [CrossRef]
  16. Q. Liu and X. Zhang, “Secure 3D watermarking algorithm based on point set projection,” Proc. SPIE-Int. Soc. Opt. Eng. 6790, 67904R (2007).
  17. H. Lu, J. Zhao, Q. Fan, Y. Xu, and X. Wan, “Iterative double random phase encryption based on pixel scrambling technology,” Acta Photonica Sin. 34, 1069-1073 (2005).
  18. K. T. Lin, “Digital information encrypted in an image using binary encoding,” Opt. Commun. 281, 3447-3453(2008).
    [CrossRef]
  19. S. L. Yeh, “Dot-matrix hologram with an encrypted figure,” Opt. Eng. 45, 095801 (2006).
  20. X. Y. Yu, H. E. Ren, S. Li, and X. D. Zhang, “A new measurement method of image encryption,” J. Phys. Conf. Ser. 48, 408-411 (2006).
    [CrossRef]
  21. M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226-239(1999).
    [CrossRef]
  22. T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image in paint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia, (Association for Computing Machinery, 2003), pp. 102-103.

2008 (3)

Y. Zhou, S. Agaian, V. M. Joyner, and K. Panetta, “Two Fibonacci p-code based image scrambling algorithms,” Proc. SPIE 6812, 681215 (2008).

R. Ye and H. Li, “A novel image scrambling and watermarking scheme based on cellular automata,” in 2008 International Symposium on Electronic Commerce and Security (2008), pp. 938-941.

K. T. Lin, “Digital information encrypted in an image using binary encoding,” Opt. Commun. 281, 3447-3453(2008).
[CrossRef]

2007 (4)

Y. Y. Wang, Y. R. Wang, Y. Wang, H. J. Li, and W. J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761-765 (2007).
[CrossRef]

Q. Liu and X. Zhang, “Secure 3D watermarking algorithm based on point set projection,” Proc. SPIE-Int. Soc. Opt. Eng. 6790, 67904R (2007).

H. Zhang, J. Huang, and Z. Li, “New method of digital image scrambling based on binary tree generated by chaotic sequences,” Proc. SPIE 6790, 67905D (2007).

J. Zhao, H. Lu, and Q. Fan, “Color image encryption based on fractional Fourier transforms and pixel scrambling technique,” Proc. SPIE 6279, 62793B (2007).

2006 (4)

X. F. Meng, L. Z. Cai, X. L. Yang, X. X. Shen, and G. Y. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45, 3289 (2006).
[CrossRef]

Y. L. Yang, N. Cai, and G. Q. Ni, “Digital image scrambling technology based on the symmetry of Arnold transform,” J. Beijing Inst. Technol. 15, 216-220 (2006).

S. L. Yeh, “Dot-matrix hologram with an encrypted figure,” Opt. Eng. 45, 095801 (2006).

X. Y. Yu, H. E. Ren, S. Li, and X. D. Zhang, “A new measurement method of image encryption,” J. Phys. Conf. Ser. 48, 408-411 (2006).
[CrossRef]

2005 (3)

H. Lu, J. Zhao, Q. Fan, Y. Xu, and X. Wan, “Iterative double random phase encryption based on pixel scrambling technology,” Acta Photonica Sin. 34, 1069-1073 (2005).

B. Li and J. W. Xu, “Period of Arnold transformation and its application in image scrambling,” J. Cent. South Univ. Technol. 12, 278-282 (2005).

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493-499(2005).
[CrossRef]

2004 (1)

T. Kong and D. Zhang, “A new anti-Arnold transformation algorithm,” J. Software 15, 1558-1564 (2004).

2003 (2)

T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image in paint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia, (Association for Computing Machinery, 2003), pp. 102-103.

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fraction Fourier domains,” Opt. Lett. 28, 269-271 (2003).
[CrossRef]

2002 (1)

C. C. Chang and J. C. Chuang, “An image intellectual property protection scheme for gray-level images using visual secret sharing strategy,” Pattern Recognit. Lett. 23, 931-941 (2002).
[CrossRef]

2000 (1)

D. Qi, J. Zou, and X. Han, “A new class of scrambling transformation and its application in the image information covering,” Sci. China Ser. E Technol. Sci. 43, 304-312 (2000).

1999 (1)

M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226-239(1999).
[CrossRef]

1997 (1)

O. Lafe, “Data compression and encryption using cellular automata transforms,” Eng. Applic. Artif. Intell. 10, 581-591(1997).

1996 (1)

G. Z. Hernández and H. J. Herrmann, “Cellular automata for elementary image enhancement,” Graphical Models Image Process. 58, 82-89 (1996).

Agaian, S.

Y. Zhou, S. Agaian, V. M. Joyner, and K. Panetta, “Two Fibonacci p-code based image scrambling algorithms,” Proc. SPIE 6812, 681215 (2008).

Cai, L. Z.

Cai, N.

Y. L. Yang, N. Cai, and G. Q. Ni, “Digital image scrambling technology based on the symmetry of Arnold transform,” J. Beijing Inst. Technol. 15, 216-220 (2006).

Chang, C. C.

C. C. Chang and J. C. Chuang, “An image intellectual property protection scheme for gray-level images using visual secret sharing strategy,” Pattern Recognit. Lett. 23, 931-941 (2002).
[CrossRef]

Chang, R. C.

T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image in paint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia, (Association for Computing Machinery, 2003), pp. 102-103.

Chuang, J. C.

C. C. Chang and J. C. Chuang, “An image intellectual property protection scheme for gray-level images using visual secret sharing strategy,” Pattern Recognit. Lett. 23, 931-941 (2002).
[CrossRef]

Dong, G. Y.

Fan, Q.

J. Zhao, H. Lu, and Q. Fan, “Color image encryption based on fractional Fourier transforms and pixel scrambling technique,” Proc. SPIE 6279, 62793B (2007).

H. Lu, J. Zhao, Q. Fan, Y. Xu, and X. Wan, “Iterative double random phase encryption based on pixel scrambling technology,” Acta Photonica Sin. 34, 1069-1073 (2005).

Han, X.

D. Qi, J. Zou, and X. Han, “A new class of scrambling transformation and its application in the image information covering,” Sci. China Ser. E Technol. Sci. 43, 304-312 (2000).

Hennelly, B.

Hernández, G. Z.

G. Z. Hernández and H. J. Herrmann, “Cellular automata for elementary image enhancement,” Graphical Models Image Process. 58, 82-89 (1996).

Herrmann, H. J.

G. Z. Hernández and H. J. Herrmann, “Cellular automata for elementary image enhancement,” Graphical Models Image Process. 58, 82-89 (1996).

Huang, J.

H. Zhang, J. Huang, and Z. Li, “New method of digital image scrambling based on binary tree generated by chaotic sequences,” Proc. SPIE 6790, 67905D (2007).

Joyner, V. M.

Y. Zhou, S. Agaian, V. M. Joyner, and K. Panetta, “Two Fibonacci p-code based image scrambling algorithms,” Proc. SPIE 6812, 681215 (2008).

Kong, T.

T. Kong and D. Zhang, “A new anti-Arnold transformation algorithm,” J. Software 15, 1558-1564 (2004).

Kutter, M.

M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226-239(1999).
[CrossRef]

Lafe, O.

O. Lafe, “Data compression and encryption using cellular automata transforms,” Eng. Applic. Artif. Intell. 10, 581-591(1997).

Li, B.

B. Li and J. W. Xu, “Period of Arnold transformation and its application in image scrambling,” J. Cent. South Univ. Technol. 12, 278-282 (2005).

Li, H.

R. Ye and H. Li, “A novel image scrambling and watermarking scheme based on cellular automata,” in 2008 International Symposium on Electronic Commerce and Security (2008), pp. 938-941.

Li, H. J.

Y. Y. Wang, Y. R. Wang, Y. Wang, H. J. Li, and W. J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761-765 (2007).
[CrossRef]

Li, J.

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493-499(2005).
[CrossRef]

Li, S.

X. Y. Yu, H. E. Ren, S. Li, and X. D. Zhang, “A new measurement method of image encryption,” J. Phys. Conf. Ser. 48, 408-411 (2006).
[CrossRef]

Li, Z.

H. Zhang, J. Huang, and Z. Li, “New method of digital image scrambling based on binary tree generated by chaotic sequences,” Proc. SPIE 6790, 67905D (2007).

Lin, K. T.

K. T. Lin, “Digital information encrypted in an image using binary encoding,” Opt. Commun. 281, 3447-3453(2008).
[CrossRef]

Liu, Q.

Q. Liu and X. Zhang, “Secure 3D watermarking algorithm based on point set projection,” Proc. SPIE-Int. Soc. Opt. Eng. 6790, 67904R (2007).

Lu, H.

J. Zhao, H. Lu, and Q. Fan, “Color image encryption based on fractional Fourier transforms and pixel scrambling technique,” Proc. SPIE 6279, 62793B (2007).

H. Lu, J. Zhao, Q. Fan, Y. Xu, and X. Wan, “Iterative double random phase encryption based on pixel scrambling technology,” Acta Photonica Sin. 34, 1069-1073 (2005).

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493-499(2005).
[CrossRef]

Lu, L. C.

T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image in paint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia, (Association for Computing Machinery, 2003), pp. 102-103.

Ma, Y.

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493-499(2005).
[CrossRef]

Meng, X. F.

Ni, G. Q.

Y. L. Yang, N. Cai, and G. Q. Ni, “Digital image scrambling technology based on the symmetry of Arnold transform,” J. Beijing Inst. Technol. 15, 216-220 (2006).

Panetta, K.

Y. Zhou, S. Agaian, V. M. Joyner, and K. Panetta, “Two Fibonacci p-code based image scrambling algorithms,” Proc. SPIE 6812, 681215 (2008).

Petitcolas, F. A. P.

M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226-239(1999).
[CrossRef]

Qi, D.

D. Qi, J. Zou, and X. Han, “A new class of scrambling transformation and its application in the image information covering,” Sci. China Ser. E Technol. Sci. 43, 304-312 (2000).

Ren, H. E.

X. Y. Yu, H. E. Ren, S. Li, and X. D. Zhang, “A new measurement method of image encryption,” J. Phys. Conf. Ser. 48, 408-411 (2006).
[CrossRef]

Shen, X. X.

Sheridan, J. T.

Shih, T. K.

T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image in paint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia, (Association for Computing Machinery, 2003), pp. 102-103.

Song, X.

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493-499(2005).
[CrossRef]

Sun, W. J.

Y. Y. Wang, Y. R. Wang, Y. Wang, H. J. Li, and W. J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761-765 (2007).
[CrossRef]

Wan, X.

H. Lu, J. Zhao, Q. Fan, Y. Xu, and X. Wan, “Iterative double random phase encryption based on pixel scrambling technology,” Acta Photonica Sin. 34, 1069-1073 (2005).

Wang, Y.

Y. Y. Wang, Y. R. Wang, Y. Wang, H. J. Li, and W. J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761-765 (2007).
[CrossRef]

Wang, Y. R.

Y. Y. Wang, Y. R. Wang, Y. Wang, H. J. Li, and W. J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761-765 (2007).
[CrossRef]

Wang, Y. Y.

Y. Y. Wang, Y. R. Wang, Y. Wang, H. J. Li, and W. J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761-765 (2007).
[CrossRef]

Xu, J. W.

B. Li and J. W. Xu, “Period of Arnold transformation and its application in image scrambling,” J. Cent. South Univ. Technol. 12, 278-282 (2005).

Xu, Y.

H. Lu, J. Zhao, Q. Fan, Y. Xu, and X. Wan, “Iterative double random phase encryption based on pixel scrambling technology,” Acta Photonica Sin. 34, 1069-1073 (2005).

Yang, X. L.

Yang, Y. L.

Y. L. Yang, N. Cai, and G. Q. Ni, “Digital image scrambling technology based on the symmetry of Arnold transform,” J. Beijing Inst. Technol. 15, 216-220 (2006).

Ye, R.

R. Ye and H. Li, “A novel image scrambling and watermarking scheme based on cellular automata,” in 2008 International Symposium on Electronic Commerce and Security (2008), pp. 938-941.

Yeh, S. L.

S. L. Yeh, “Dot-matrix hologram with an encrypted figure,” Opt. Eng. 45, 095801 (2006).

Yu, X. Y.

X. Y. Yu, H. E. Ren, S. Li, and X. D. Zhang, “A new measurement method of image encryption,” J. Phys. Conf. Ser. 48, 408-411 (2006).
[CrossRef]

Zhang, D.

T. Kong and D. Zhang, “A new anti-Arnold transformation algorithm,” J. Software 15, 1558-1564 (2004).

Zhang, H.

H. Zhang, J. Huang, and Z. Li, “New method of digital image scrambling based on binary tree generated by chaotic sequences,” Proc. SPIE 6790, 67905D (2007).

Zhang, X.

Q. Liu and X. Zhang, “Secure 3D watermarking algorithm based on point set projection,” Proc. SPIE-Int. Soc. Opt. Eng. 6790, 67904R (2007).

Zhang, X. D.

X. Y. Yu, H. E. Ren, S. Li, and X. D. Zhang, “A new measurement method of image encryption,” J. Phys. Conf. Ser. 48, 408-411 (2006).
[CrossRef]

Zhao, J.

J. Zhao, H. Lu, and Q. Fan, “Color image encryption based on fractional Fourier transforms and pixel scrambling technique,” Proc. SPIE 6279, 62793B (2007).

H. Lu, J. Zhao, Q. Fan, Y. Xu, and X. Wan, “Iterative double random phase encryption based on pixel scrambling technology,” Acta Photonica Sin. 34, 1069-1073 (2005).

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493-499(2005).
[CrossRef]

Zhou, Y.

Y. Zhou, S. Agaian, V. M. Joyner, and K. Panetta, “Two Fibonacci p-code based image scrambling algorithms,” Proc. SPIE 6812, 681215 (2008).

Zou, J.

D. Qi, J. Zou, and X. Han, “A new class of scrambling transformation and its application in the image information covering,” Sci. China Ser. E Technol. Sci. 43, 304-312 (2000).

Acta Photonica Sin. (1)

H. Lu, J. Zhao, Q. Fan, Y. Xu, and X. Wan, “Iterative double random phase encryption based on pixel scrambling technology,” Acta Photonica Sin. 34, 1069-1073 (2005).

Appl. Opt. (1)

Eng. Applic. Artif. Intell. (1)

O. Lafe, “Data compression and encryption using cellular automata transforms,” Eng. Applic. Artif. Intell. 10, 581-591(1997).

Graphical Models Image Process. (1)

G. Z. Hernández and H. J. Herrmann, “Cellular automata for elementary image enhancement,” Graphical Models Image Process. 58, 82-89 (1996).

J. Beijing Inst. Technol. (1)

Y. L. Yang, N. Cai, and G. Q. Ni, “Digital image scrambling technology based on the symmetry of Arnold transform,” J. Beijing Inst. Technol. 15, 216-220 (2006).

J. Cent. South Univ. Technol. (1)

B. Li and J. W. Xu, “Period of Arnold transformation and its application in image scrambling,” J. Cent. South Univ. Technol. 12, 278-282 (2005).

J. Phys. Conf. Ser. (1)

X. Y. Yu, H. E. Ren, S. Li, and X. D. Zhang, “A new measurement method of image encryption,” J. Phys. Conf. Ser. 48, 408-411 (2006).
[CrossRef]

J. Software (1)

T. Kong and D. Zhang, “A new anti-Arnold transformation algorithm,” J. Software 15, 1558-1564 (2004).

Opt. Commun. (2)

J. Zhao, H. Lu, X. Song, J. Li, and Y. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493-499(2005).
[CrossRef]

K. T. Lin, “Digital information encrypted in an image using binary encoding,” Opt. Commun. 281, 3447-3453(2008).
[CrossRef]

Opt. Eng. (1)

S. L. Yeh, “Dot-matrix hologram with an encrypted figure,” Opt. Eng. 45, 095801 (2006).

Opt. Lasers Eng. (1)

Y. Y. Wang, Y. R. Wang, Y. Wang, H. J. Li, and W. J. Sun, “Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology,” Opt. Lasers Eng. 45, 761-765 (2007).
[CrossRef]

Opt. Lett. (1)

Pattern Recognit. Lett. (1)

C. C. Chang and J. C. Chuang, “An image intellectual property protection scheme for gray-level images using visual secret sharing strategy,” Pattern Recognit. Lett. 23, 931-941 (2002).
[CrossRef]

Proc. SPIE (4)

H. Zhang, J. Huang, and Z. Li, “New method of digital image scrambling based on binary tree generated by chaotic sequences,” Proc. SPIE 6790, 67905D (2007).

J. Zhao, H. Lu, and Q. Fan, “Color image encryption based on fractional Fourier transforms and pixel scrambling technique,” Proc. SPIE 6279, 62793B (2007).

M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” Proc. SPIE 3657, 226-239(1999).
[CrossRef]

Y. Zhou, S. Agaian, V. M. Joyner, and K. Panetta, “Two Fibonacci p-code based image scrambling algorithms,” Proc. SPIE 6812, 681215 (2008).

Proc. SPIE-Int. Soc. Opt. Eng. (1)

Q. Liu and X. Zhang, “Secure 3D watermarking algorithm based on point set projection,” Proc. SPIE-Int. Soc. Opt. Eng. 6790, 67904R (2007).

Sci. China Ser. E Technol. Sci. (1)

D. Qi, J. Zou, and X. Han, “A new class of scrambling transformation and its application in the image information covering,” Sci. China Ser. E Technol. Sci. 43, 304-312 (2000).

Other (2)

R. Ye and H. Li, “A novel image scrambling and watermarking scheme based on cellular automata,” in 2008 International Symposium on Electronic Commerce and Security (2008), pp. 938-941.

T. K. Shih, L. C. Lu, and R. C. Chang, “An automatic image in paint tool,” in Proceedings of the Eleventh ACM International Conference on Multimedia, (Association for Computing Machinery, 2003), pp. 102-103.

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Figures (12)

Fig. 1
Fig. 1

Example for pixel scrambling from C to D . (a)  C , (b)  A , (c)  D for n = 2 , (d)  D for n = 3 .

Fig. 2
Fig. 2

Example for pixel descrambling from D * to C * . (a)  D * , (b)  C * for n = 2 , (c)  C * for n = 3 .

Fig. 3
Fig. 3

(a) Assumed host matrix H , (b) assumed binary matrix T , (c) resulting modulated matrix H , (d) resulting overt image H * .

Fig. 4
Fig. 4

Covert images for tests. (a)  64 × 120 120 binary image, (b)  64 × 120 256-gray-level image.

Fig. 5
Fig. 5

Host image for encoding to form different overt images.

Fig. 6
Fig. 6

(a) Matrix D with n = 17 and t = 5 , (b) matrix T with n = 17 and t = 5 , (c) overt matrix H * for encoding the covert image in Fig. 4a.

Fig. 7
Fig. 7

(a) Matrix D with n = 14 and t = 2 , (b) matrix T with n = 14 and t = 2 .

Fig. 8
Fig. 8

Image scrambling degrees with different n values and t = 1 for (a) Fig. 4a and (b) Fig. 4b.

Fig. 9
Fig. 9

Image scrambling degrees with different t values and (a)  n = 7 for Fig. 4a, (b)  n = 20 for Fig. 4b.

Fig. 10
Fig. 10

Conditions for image scrambling degree percentages greater than 80% for (a) Fig. 4a and (b) Fig. 4b.

Fig. 11
Fig. 11

Different scrambled Lena images for t = 1 by using (a) the p-Fibonacci transformation, (b) the Arnold transformation, (c) the proposed method.

Fig. 12
Fig. 12

Image scrambling degree percentages for t = 1 for (a) the p-Fibonacci transformation and (b) the Arnold transformation.

Equations (12)

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

k = i = 1 8 k i × 2 i 1 + k 0 .
E ( ( r 1 ) × c + c ) = D ( r , c ) ,
G ( i + h × ( k 1 ) ) = a i ( k ) .
H ( u , v ) = 2  floor ( H ( u , v ) / 2 ) ,
H * ( u , v ) = T ( u , v ) + H ( u , v ) .
T ( m , n ) = H * ( m , n ) 2  floor ( H * ( m , n ) / 2 ) ,
E ( k ) = m = 1 m G ( m ( k 1 ) + m ) 2 m m ,
D * ( r , c ) = E ( ( r 1 ) × c + c ) .
δ = i = 1 r j = 1 c [ K 1 , 0 ( i , j ) + K 1 , 0 ( i , j ) + K 0 , 1 ( i , j ) + K 0 , 1 ( i , j ) ] 255 2 × r × c ,
K m , n = | [ D ( i + m , j + n ) D ( i , j ) ] 2 [ C ( i + m , j + n ) C ( i , j ) ] 2 | .
PSNR = 10 × log ( M × N MSE ) ,
MSE = 1 M × N i = 1 M j = 1 N [ H ( i , j ) H * ( i , j ) ] 2 .

Metrics