Commutative Encryption and Watermarking Algorithm for High-Resolution Remote Sensing Images Based on Homomorphic Encryption

Yu Li; Liming Zhang; Hao Wang; Xiaolong Wang

doi:10.3788/LOP202259.1815012

Laser & Optoelectronics Progress, Volume. 59, Issue 18, 1815012(2022)

Commutative Encryption and Watermarking Algorithm for High-Resolution Remote Sensing Images Based on Homomorphic Encryption

Yu Li^1,2,3, Liming Zhang^1,2,3、*, Hao Wang^1,2,3, and Xiaolong Wang^1,2,3

Author Affiliations

¹Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu , China

²National-Local Joint Engineering Research Center of Technologies and Applications for National Geographic State Monitoring, Lanzhou 730070, Gansu , China

³Gansu Provincial Engineering Laboratory for National Geographic State Monitoring, Lanzhou 730070, Gansu , China

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Figures & Tables(14)

Fig. 1. CEW algorithm model for HRRS image

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Fig. 2. Division of HRRS image

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Fig. 3. Original images. (a) Image A; (b) image B; (c) image C

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Fig. 4. Watermark images. (a) Original watermark; (b) shuffled watermark

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Fig. 5. CEW experiment results. (a)-(c) CEWed image (A1, B1, C1); (d)-(f) D-Wed image (A2, B2, C2)

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Fig. 6. Analysis result of key sensitivity. (a)-(c) CEWed image (A3, B3, C3) with the key p_k2; (d)-(f) D-Wed image (A4, B4, C4) with s_k2

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Fig. 7. Comparison result of imperceptibility

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Fig. 8. Comparison result of robustness

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Table 1. MAE of CEWed/D-Wed images using different secret keys
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Table 1. MAE of CEWed/D-Wed images using different secret keys
HRRS image MAE between CEWed images MAE between D-Wed images
A 9.58×10¹⁴ 2.55×10⁷
B 9.39×10¹⁴ 2.39×10⁷
C 9.06×10¹⁴ 2.01×10⁷

Table 2. Adjacent pixel correlation between original images and encrypted images
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Table 2. Adjacent pixel correlation between original images and encrypted images
Direction Original image CEWed image
A B C A1 B1 C1
Horizontal 0.9685 0.9657 0.9479 0.0065 0.0118 0.0521
Vertical 0.9755 0.9723 0.9274 0.0809 0.0991 0.0855
Diagonal 0.9506 0.9462 0.8936 -0.0038 0.0072 0.0311

Table 3. PSNR of D-Wed images with different embedding intensities
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Table 3. PSNR of D-Wed images with different embedding intensities
Embedding strength A2 B2 C2
1 48.0967 47.2722 48.0991
2 42.0769 41.2517 42.0784
3 38.5568 37.7299 38.5599

Table 4. Experimental results of robustness

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Table 4. Experimental results of robustness

Parameter		No attack	Salt-and-pepper noise	Gaussian noise	Median filtering	Upper part cut	Arbitrary cut	Arbitrary cut
Parameter		No attack	0.01	0.003	3×3	1/2	1/8	1/4
NC	A2	1.0	0.9803	0.9848	0.8793	1.0	1.0	0.9675
	B2	1.0	0.9805	0.9839	0.8971	1.0	1.0	0.9838
	C2	1.0	0. 9805	0.9843	0.9266	1.0	1.0	1.0

Table 5. Comparison of algorithm running time
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Table 5. Comparison of algorithm running time
Procedure Proposed CEW algorithm CEW algorithm in Ref.［26］
A B C A B C
Encryption and watermark embedding 2.2 8.9 35.7 8.7 45.6 98.6
Decryption and watermark extraction 3.2 13.5 55.4 10.5 49.2 105.9

Table 6. Result of accuracy evaluation
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Table 6. Result of accuracy evaluation
Parameter D-Wed image A2 D-Wed image B2 D-Wed image C2
OA /% 99.4835 99.1806 99.2253
Kappa coefficient 0.9933 0.9896 0.9898

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Yu Li, Liming Zhang, Hao Wang, Xiaolong Wang. Commutative Encryption and Watermarking Algorithm for High-Resolution Remote Sensing Images Based on Homomorphic Encryption[J]. Laser & Optoelectronics Progress, 2022, 59(18): 1815012

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