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

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 18 >Page 1815012 > Article

Laser & Optoelectronics Progress
Vol. 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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DOI: 10.3788/LOP202259.1815012 Cite this Article Set citation alerts

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 Copy Citation Text

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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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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 1. MAE of CEWed/D-Wed images using different secret keys

Direction	Original image			CEWed image
Direction	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 2. Adjacent pixel correlation between original images and encrypted images

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 3. PSNR of D-Wed images with different embedding intensities

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 4. Experimental results of robustness

Procedure	Proposed CEW algorithm			CEW algorithm in Ref.［26］
Procedure	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 5. Comparison of algorithm running time

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

Table 6. Result of accuracy evaluation

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