Fig 1.
Flowchart of the proposed image encryption algorithm.
Fig 2.
Division of the plain-image.
Fig 3.
Shuffling of the image blocks Blk. 1 and Blk. 4.
Fig 4.
The chaotic behaviors of systems (2) and (3).
(a) The spatiotemporal attractor of the 2D CML (2) with μ = 1.8 and ε = 0.1, (b) the chaotic attractor of the fractional-order Chen system (3) with α1 = α2 = α3 = 0.9.
Fig 5.
Experimental results for Lena image.
(a) Original image of Lena, (b) encrypted image of Lena, (c) decrypted image of Lena.
Fig 6.
Experimental results for Vegetables image.
(a) Original image of Vegetables, (b) encrypted image of Vegetables, (c) decrypted image of Vegetables.
Fig 7.
Histogram of the original image of Lena in the (a) red, (b) green, (c) blue, components.
Fig 8.
Histogram of the encrypted image of Lena in the (a) red, (b) green, (c) blue, components.
Fig 9.
Vertical direction correlations of two adjacent pixels.
Frames (a), (c) and (e) show the distribution of two vertically adjacent pixels in the plain-image of Lena in the (a) red, (b) green and (c) blue components, respectively. Frames (b), (d) and (f) display the distribution of two vertically adjacent pixels in the encrypted image of Lena in the (b) red, (d) green and (f) blue components, respectively.
Table 1.
Correlation coefficients of two adjacent pixels in the plain-image and cipher-image.
Table 2.
Comparison of correlation coefficients of two adjacent pixels in different directions using the proposed algorithm with some other algorithms.
Table 3.
Comparison of the information entropy using the proposed algorithm with some other algorithms.
Fig 10.
NPCR and UACI performance analysis of the proposed scheme.
(a) NPCR versus permutation rounds, (b) UACI versus permutation rounds.
Table 4.
NPCR and UACI of the color image of Lena when changing one pixel and permutation rounds n = 10.
Table 5.
Comparison of the average NPCR and UACI values on the color image of Lena.
Fig 11.
(a) Original image of Lena, (b) encrypted image of Lena with the secret key K1, (c) encrypted image of Lena with the secret key K2, (d) difference image.
Fig 12.
(a) Encrypted image of Lena with the secret key K1, (b) decrypted image with the secret key K2, (c) decrypted image with the secret key K1, (d) encrypted image of Lena with the secret key K2, (e) decrypted image with the secret key K1, (f) decrypted image with the secret K2.
Fig 13.
Some original plain-images used in Table 6.
(a) City gate tower, (b) Elephantine mountain, (c) Pandas, (d) Peony.
Table 6.
Comparison of pixel difference between images encrypted by keys with one-bit difference.
Table 7.
Comparison of encryption time between our proposed method and some other cryptosystems.
Table 8.
The PSNR of decrypted image under different image processing operations.
Fig 14.
(a) Original image of Lena, (b) encrypted image of Lena without noise addition, (c) encrypted image of Lena under adding Pepper & Salt noise with noise density 0.005, (d) decrypted image under Pepper & Salt noise addition (noise density 0.005), (e) encrypted image of Lena under adding Pepper & Salt noise with noise density 0.05, (f) decrypted image under Pepper & Salt noise addition (noise density 0.05), (g) encrypted image of Lena under adding Pepper & Salt noise with noise density 0.5, (h) decrypted image under Pepper & Salt noise addition (noise density 0.5), (i) encrypted image of Lena under Gaussian white noise addition, (j) decrypted image under Gaussian white noise addition.
Fig 15.
(a) Cropped cipher-mage by removing 25% of the encrypted image of Lena (Fig. 14(b)), (b) decrypted image of the cropped cipher-image (a), (c) cropped cipher-mage by removing 50% of the encrypted image of Lena (Fig. 14(b)), (d) decrypted image of the cropped cipher-image (c).
Fig 16.
Test of image encryption with JPEG compression.
(a) JPEG compressed cipher-mage of Lena, (b) decrypted image under JPEG compression.
Fig 17.
(a) Rotated cipher-image of Lena, (b) decrypted image under rotation.
Fig 18.
Test of image under brightening and darkening.
(a) Brightened cipher-image of Lena, (b) decrypted image under brightening, (c) darkened cipher-image of Lena, (d) decrypted image under darkening.