A Secure Outsourcing Search Scheme for Encrypted Remote Sensing Images

Fig. 11. Search results of remote sensing images. (a) Image O; (b) image with different phases; (c) remote sensing image with Gaussian noise; (d) remote sensing image under dimmed light; (e) remote sensing image with deformation; (f) remote sensing image of island; (g) remote sensing image of land

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Fig. 12. Comparison of precision rates

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Fig. 13. Comparison of recall rates

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Fig. 14. Comparison of search time

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Fig. 15. Binary attack effect. (a) Basic scheme; (b) improved scheme

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Fig. 16. Correlation among adjacent pixels in original image

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Fig. 17. Correlation among adjacent pixels in encrypted image

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Table 1. Algorithm 1 of encryption algorithm for remote sensing images

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Table 1. Algorithm 1 of encryption algorithm for remote sensing images

Input	Split an index remote sensing image band into a single-band image Y(i,j);Height and width of remote sensing image are H and W;Randomly generate a matrix Q of Gaussian distribution h²×k obeying an average of 0 and a variance of 1/k;Randomly generate a matrix R of H×W;Randomly generate a matrix Δ of h²×k;
Ouput	XOR encrypted remote sensing image E_A;JL transformation encrypted remote sensing image E_B;Double ciphertext E_B={E_A,E_B}
Algorithmicprocess	1. for image Y i=1 to H {2. for image Y j=1 to W {3. E_A(i,j)=Y(i,j)⊕R(i,j)4. }5. }6. for image Y i=1 to h²{7. for image Y j=1 to h²{8. for matrix Q m=1 to h²{9. for matrix Q n=1 to k {10. E_B(m,n)=Y(i,j)×Q(m,n)+Δ(m,n)11. }12. }13. }14. }15. return upload index E_I={E_A,E_B}

Table 2. Algorithm 2 of algorithm for calculation of Euclidean distance between remote sensing images

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Table 2. Algorithm 2 of algorithm for calculation of Euclidean distance between remote sensing images

Input	Height and width of remote sensing image E_B by JL transformation are H and W; Remote sensing image S stored in cloud platform;
Ouput	Distance of two remote sensing images is d;
Algorithmicprocess	1. for image E_B i=1 to H {2. for image E_B j=1 to W {3. sum+=(E_B(i,j)-S(i,j))²4. }5. }6. d= $\begin{matrix} \sqrt[]{\|\frac{sum - 2 \times k \times ξ^{2}}{h^{2}}\|} \end{matrix}$ 7. return distance d

Table 3. Optimal threshold analysis

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Table 3. Optimal threshold analysis

(T₁,T₂)	Actual number ofsimilar images	Number ofimages searched	Number ofcorrect images	Number oferror images	Number of imagesnot searched
(0.7,0.8)	56	0	0	0	56
(0.8,0.9)	56	0	0	0	56
(0.9,1.0)	56	4	4	0	52
(1.0,1.1)	56	12	12	0	44
(1.1,1.2)	56	52	32	20	24
(1.2,1.3)	56	56	0	56	56
(0.8,1.0)	56	4	4	0	52
(0.9,1.1)	56	20	20	0	36
(1.0,1.2)	56	64	44	20	12
(0.8,1.1)	56	20	20	0	36
(0.9,1.2)	56	72	52	20	4

Table 4. Parameter value

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Table 4. Parameter value

Parameter	Instructions	Value
H	Height of remote sensing image	512
W	Width of remote sensing image	512
N	Band number of remote sensing image	200
h	Height of JL transformation	5
k	Variance parameter ofGaussian distribution Q	18
s	Variance parameter ofGaussian distribution Δ	0.5
T	Threshold	550

Table 5. Precision rate

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Table 5. Precision rate

Scheme category	Number of images
Scheme category	50	100	150	200	250	300	350	400
Lowe's scheme^[25]	0.135	0.229	0.378	0.446	0.568	0.608	0.676	0.729
Basic scheme	0.059	0.101	0.166	0.196	0.25	0.268	0.304	0.333
Improved scheme	0.139	0.222	0.375	0.431	0.556	0.597	0.667	0.722

Table 6. Recall rate

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Table 6. Recall rate

Scheme category	Number of images
Scheme category	50	100	150	200	250	300	350	400
Lowe's scheme^[25]	0.179	0.304	0.500	0.589	0.750	0.804	0.893	0.964
Basic scheme	0.179	0.304	0.500	0.589	0.750	0.804	0.911	1
Improved scheme	0.179	0.286	0.482	0.554	0.714	0.768	0.857	0.929

Table 7. Adjacent pixel point data in original and encrypted images

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Table 7. Adjacent pixel point data in original and encrypted images

Original image	Pixel value of point(x, y)	156	139	143	138	139	147	153	156	157	146
Original image	Pixel value of point (x+1, y)	77	57	71	56	48	49	61	78	81	91
Encrypted image	Pixel value of point(x,y)	156	139	143	138	139	147	153	156	151	156
Encrypted image	Pixel value of point (x+1, y)	33	111	19	63	47	114	24	88	37	32

Table 8. Analysis of related schemes for ciphertext search

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Table 8. Analysis of related schemes for ciphertext search

Ciphertextsearch scheme	Suitable forcloud computing	Support imagesearch	Security	Accuracy	Searchefficiency
Ref. [26]	Yes	False	Low	Low	Low
Ref. [27]	False	False	High	High	Low
Ref. [28]	False	Yes	Low	High	Low
Ref. [13]	Yes	Yes	Higher	High	Higher
Proposed scheme	Yes	Yes	High	High	High

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Dongmei Huang, Guojian Wu, Lifei Wei, Quanmiao Wei, Liang Dai. A Secure Outsourcing Search Scheme for Encrypted Remote Sensing Images[J]. Laser & Optoelectronics Progress, 2019, 56(3): 031001

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Paper Information

Category: Image Processing

Received: Jun. 5, 2018

Accepted: Aug. 11, 2018

Published Online: Jul. 31, 2019

The Author Email: Lifei Wei (Lfwei@shou.edu.cn)

DOI:10.3788/LOP56.031001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology