Author Affiliations
1Information Engineering College, Capital Normal University, Beijing 100048, China2Department of Physics, Capital Normal University, Beijing 100048, China3Beijing Advanced Innovation Center for Imaging Theory and Technology, Beijing 100048, Chinashow less
Fig. 1. Flowchart of the proposed algorithm. (a) Encryption process; (b) decryption process
Fig. 2. Tested images. (a) Lena; (b) Elephant; (c) Grnpeace; (d) Peppers; (e) Butterfly
Fig. 3. Results of encryption and decryption. (a) Cipherimages; (b) restituted images
Fig. 4. Histogram results. (a) Plaintext images; (b) ciphertext images
Fig. 5. Correlation distribution of adjacent pixels. (a) Lena's plaintext image; (b) Lena's ciphertext image
Fig. 6. Results of chosen-plaintext attack. (a) Fake plaintext images; (b) decrypted results of Fig.3(a)
Fig. 7. Decrypted results using a slightly deviated key. (a) a; (b) b; (c) c; (d) x'0
Fig. 8. Decrypted results when the intensity of Gaussian noise is 1. (a) Proposed algorithm; (b) algorithm in Ref.[16]; (c) algorithm in Ref.[17]
Fig. 9. Average PSNR and CC under Gaussian noise attack. (a) PSNR; (b) CC
Fig. 10. Decrypted images under cropping attack(η=20%). (a) Proposed algorithm; (b) algorithm in Ref.[16]; (c) algorithm in Ref.[17]
Fig. 11. Average PSNR and CC under cropping attack. (a) PSNR; (b) CC
Image | Proposed algorithm | Algorithm in Ref. [16] | Algorithm in Ref. [17] |
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1D-DFT | 2D-DFT |
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2×2 | 2×3 | 3×2 | 2×2 | 2×3 | 3×2 | Lena | 300.4656 | 291.7590 | 287.9488 | 298.4824 | 289.0684 | 295.0256 | 262.7863 | 302.4648 | Elephant | 291.8283 | 294.5651 | 303.3073 | 293.4864 | 300.8966 | 299.7538 | 272.0697 | 304.3388 | Grnpeace | 315.7956 | 293.4830 | 286.2010 | 311.1888 | 291.8217 | 296.4422 | 253.9804 | 308.4498 | Peppers | 296.8666 | 290.3514 | 283.4614 | 296.7653 | 292.6517 | 282.7151 | 259.1771 | 303.3361 | Butterfly | 304.7186 | 296.1617 | 294.6717 | 301.7734 | 298.5181 | 298.4478 | 243.4396 | 304.2931 | Mean/standard deviation | 301.9349/ 9.0810 | 293.2640/ 2.2850 | 291.1180/ 7.9695 | 300.3393/ 6.7630 | 294.5913/ 4.9273 | 294.4769/ 6.8212 | 258.2906/ 10.6065 | 304.5765/ 2.2988 |
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Table 1. PSNR of correctly decryption
Image | Horizontal | Vertical | Diagonal |
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Lena in Fig.2 | 0.9469 | 0.9088 | 0.8829 | Elephant in Fig.2 | 0.9645 | 0.9519 | 0.9319 | Grnpeace in Fig.2 | 0.7127 | 0.7933 | 0.7001 | Peppers in Fig.2 | 0.9469 | 0.9407 | 0.9289 | Butterfly in Fig.2 | 0.8776 | 0.8930 | 0.8386 | Lena in Fig.3(a) | 0.0156 | 0.1012 | -0.0047 | Elephant in Fig.3(a) | 0.0440 | 0.0564 | -0.0013 | Grnpeace in Fig.3(a) | 0.0377 | -0.0119 | 0.0042 | Peppers in Fig.3(a) | 0.0449 | 0.0018 | -0.0010 | Butterfly in Fig.3(a) | -0.0419 | 0.0165 | 0.0238 |
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Table 2. Correlation coefficients of plaintext and ciphertext images