JPEG encryption for image rescaling in the encrypted domain

Accepted Manuscript Short communication JPEG Encryption for Image Rescaling in the Encrypted Domain Zhenxing Qian, Xinpeng Zhang, Yanli Ren PII: DOI: Reference:

S1047-3203(14)00167-9 http://dx.doi.org/10.1016/j.jvcir.2014.10.008 YJVCI 1433

To appear in:

J. Vis. Commun. Image R.

Received Date:

16 February 2014

Please cite this article as: Z. Qian, X. Zhang, Y. Ren, JPEG Encryption for Image Rescaling in the Encrypted Domain, J. Vis. Commun. Image R. (2014), doi: http://dx.doi.org/10.1016/j.jvcir.2014.10.008

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JPEG Encryption for Image Rescaling in the Encrypted Domain Zhenxing Qian, Xinpeng Zhang, Yanli Ren School of Communication and Information Engineering, Shanghai University, Shanghai 200444 E-mail: {zxqian, xzhang, renyanli}@shu.edu.cn

Abstract: This work proposes a novel protocol of encrypting the JPEG image suitable for image rescaling in the encrypted domain. To protect the privacy of original content, the image owner perturbs the texture and randomizes the structure of the JPEG image by enciphering the quantized Discrete Cosine Transform (DCT) coefficients. After receiving the encrypted JPEG image, the service provider generates a rescaled JPEG image by down-sampling the encrypted DCT coefficients. On the recipient side, the encrypted JPEG image rescaled by the service provider can be decrypted to a plaintext image with a lower resolution with the aid of encryption keys. Experimental results show that the proposed method has a good capability of rescaling the privacy-protected JPEG file. Keywords: signal processing, encrypted domain, image rescaling

1. Introduction Signal processing in encrypted domain (SPED) has attracted much attention in recent years. The need for SPED technologies originates from a growing social awareness and relevance of security and privacy [1][2]. For example, people are increasingly sharing diversity of personal data on the Internet, or doing many works over cloud computing or delegated calculation. SPED, thus, was proposed to accomplish signal processing at the potentially untrusted sites in a privacy-protected form, without or minimally leaking information [3]. Some works have been done on SPED, such as differential-privacy based sanitizing [3-5], the buyer-seller watermarking protocol [6-9], compression of the encrypted images or videos [10-13], reversible data-hiding in encrypted images [14-18], and so on [19]. While most SPED algorithms are useful for never-compressed images, few SPED methods are suitable for JPEG, which is the most widely used format. In some applications, the service provider hopes to reduce the data amount during the transmission, or tends to supply the recipient an encrypted image with a lower resolution. For example, in a dealing system, the seller

1

2 sends an encrypted image to the server platform, and the server provides the encrypted image with a lower resolution to the buyer prior to the sale completed, during which the image content is not revealed to the server. To the best of our knowledge, there’s no SPED protocol capable of rescaling the encrypted JPEG images for privacy-preserving. This paper aims to provide a SPED protocol of encrypting the JPEG formatted image, suitable for image rescaling in the encrypted domain. The proposed protocol is made up of three phases: JPEG image encryption, rescaling the encrypted JPEG image, and image decryption. Before sending a JPEG image to the remote server, the original image is encrypted to a meaningless image. On the server side, the service provider rescales the encrypted JPEG image. On the recipient side, the encrypted image is decrypted to a plaintext image with a lower resolution.

2. Proposed Protocol A sketch of the proposed protocol is given in Fig. 1, which includes three phases for the image owner, the service provider, and the recipient, respectively. The image owner generates an encrypted JPEG file by constructing a cipher mask and encrypting the quantized DCT coefficients. After receiving the encrypted JPEG file, the service provider rescales the encrypted image by down-sampling the coefficients. On the recipient side, with the encryption keys, the cipher mask is reconstructed and down-sampled as an aid to decrypt the encrypted JPEG file rescaled by the service provider. 2.1 JPEG Image Encryption For a JPEG image J that was generated by compressing a grayscale image sized M×N, the image owner encrypts J by perturbing the texture and randomizing the structure of the image content to protect the privacy of the content of J. After entropy decoding to J, the quantized DCT coefficients of each 8×8 block are extracted. Denote these coefficient blocks as Cr,s, where r=1, 2, …, M/8 and s=1, 2, …, N/8. In each block, there are 64 quantized coefficients including one DC and 63 AC coefficients. The image owner divides all the coefficients into 15 subbands, i.e. Sk={Cr,s(i, j) | k=i+j–1, 1≤i≤8, 1≤j≤8, r=1, 2, …, M/8, s=1, 2, …, N/8}, where k=1,2,…,15. For example, the subband S3 is comprised of AC coefficients on the (1,3)-th, the (2,2)-th and the (3,1)-th positions of each block. Particularly, S1 is the subband of DC coefficients. In subband Sk, there are nk coefficients, where ⎧k ⋅ MN / 64, 1 ≤ k ≤ 8 nk = ⎨ ⎩(16 − k ) ⋅ MN / 64, 9 ≤ k ≤ 15

2

3 Then, the content owner generates MN/64 pseudo-random integers with a predefined key K1, each of which is drawn from the uniform distribution on the interval [–128,128]. The generated integers are added to the MN/64 DC coefficients in S1 with the one-to-one manner. Next, he encrypts the AC coefficients in the subbands {S2, S3, …, ST-1, ST}, where T is a parameter chosen by the image owner. He generates L uniformly distributed pseudo-random integers on the interval [–R, R] with another key K2, where T

L = ∑ nk k =2

and R is a predefined positive integer. Again, with one-to-one manner, he adds the L pseudorandom integers with the AC coefficients in the subbands {S2, S3, …, ST-1, ST}. As a result, the above procedure is equivalent to add a cipher mask MS to the coefficients in C to generate a perturbed version C', where C'=C+MS and MS is sized M×N. Because the addition operation introduces many noises into the original coefficients, texture of the image content is inevitably perturbed. The image owner further divides the perturbed version of the quantized DCT coefficients in C' into MN/256 non-overlapped blocks, each of which is sized 16×16. With another key K3, he pseudo-randomly permutes the MN/256 blocks to an encrypted version E. This way, structure of the original image is randomized. It should be noted that when the image size is not an integral multiple of 16, we have to pad some zero outside the right and/or bottom boundaries for encoding, which will be removed on the recipient side. Next, by entropy encoding, the image owner compresses the encrypted DCT coefficients in E into another JPEG file J'. The encrypted file will be sent to the service provider, and the encryption keys and the parameters (K1, K2, K3, T, R) are kept by the owner. 2.2 Rescaling the Encrypted JPEG Image With the encrypted JPEG image J', although the service provider does not know the content of the image, he can still rescale the encrypted image. Since the encrypted image is in the JPEG format, the service provider first decodes the image J' into blocks of the quantized coefficients QCr,s(i, j) by entropy decoding, where r=1, 2, …, M/8, s=1, 2, …, N/8, 1≤i≤8 and 1≤j≤8. Then he extracts from the file header of J' the quantization table QT that comprises an 8×8 quantization table. Do the inverse quantization of each block with QT to reconstruct the DCT coefficients COr,s(i, j), COr,s(i, j)=QCr,s(i, j)·QT(i, j) 3

4 where r=1, 2, …, M/8, s=1, 2, …, N/8, 1≤i≤8 and 1≤j≤8. The decoded MN coefficients in CO in the encrypted form can be merged into MN/4 coefficients, meaning that the image size is reduced to 1/4 of the original. The algorithm in [20] is adopt to merge every four adjacent coefficient blocks to one coefficient block, in which the adjacent blocks X1~X4 are down-sampled to one 8×8 coefficient block X using (1).

X=

1 (U1 X1U1t + U1 X 2 U t2 + U 2 X3 U1t + U 2 X 4 U t2 ) 4

(1)

In Equation (1), U i = SQi S −1 , i = 1, 2

(2)

where ⎡1 ⎢0 ⎢ ⎢0 ⎢ 0 Q1 = ⎢ ⎢0 ⎢ ⎢0 ⎢0 ⎢ ⎢⎣0

⎡0 ⎢0 ⎢ ⎢0 ⎢ 0 Q2 = ⎢ ⎢1 ⎢ ⎢0 ⎢0 ⎢ ⎢⎣0

1 0 0 0 0 0 0⎤ 0 1 1 0 0 0 0 ⎥⎥ 0 0 0 1 1 0 0⎥ ⎥ 0 0 0 0 0 1 1⎥ 0 0 0 0 0 0 0⎥ ⎥ 0 0 0 0 0 0 0⎥ 0 0 0 0 0 0 0⎥ ⎥ 0 0 0 0 0 0 0 ⎥⎦

0 0 0 0 0 0 0⎤ 0 0 0 0 0 0 0 ⎥⎥ 0 0 0 0 0 0 0⎥ ⎥ 0 0 0 0 0 0 0⎥ 1 0 0 0 0 0 0⎥ ⎥ 0 1 1 0 0 0 0⎥ 0 0 0 1 1 0 0⎥ ⎥ 0 0 0 0 0 1 1 ⎥⎦

and S = D ⋅ P ⋅ B1 ⋅ B 2 ⋅ M ⋅ A1 ⋅ A 2 ⋅ A 3

(3)

In Equation (3), D is a diagonal matrix given by D=diag{0.3536, 0.2549, 0.2706, 0.3007, 0.3536, 0.4500, 0.6533, 1.2814} and the remaining matrices are defined as: ⎡1 ⎢0 ⎢ ⎢0 ⎢ 0 P=⎢ ⎢0 ⎢ ⎢0 ⎢0 ⎢ ⎣⎢0

0⎤ ⎡1 0 0 0 0 0 ⎥⎥ ⎢0 1 0 0 0 ⎢ 0⎥ ⎢0 0 1 0 0 ⎥ ⎢ 1⎥ ⎢0 0 0 1 0 0 ⎥ B1 = ⎢ 0 0 0 0 1 ⎥ ⎢ 0⎥ ⎢0 0 0 0 0 ⎢0 0 0 0 0 0⎥ ⎥ ⎢ 0 0 0 0 0 1 0 ⎦⎥ ⎣⎢ 0 0 0 0 −1

0 0 0 0 1 0 0

0 0 1 0 0 0 0

0 0 0 0 0 0 1

0 0 0 0 0 1 0

0 1 0 0 0 0 0

0 0 0 0 0 0 0

4

0 0 0 0 0 1 1 0

0⎤ 0 ⎥⎥ 0 0⎥ ⎥ 0 0⎥ 0 1⎥ ⎥ 1 0⎥ −1 0 ⎥ ⎥ 1 1 ⎦⎥ 0 0

⎡1 ⎢0 ⎢ ⎢0 ⎢ 0 B2 = ⎢ ⎢0 ⎢ ⎢0 ⎢0 ⎢ ⎣⎢ 0

0 1

0 0

0 0 0 0

0 1 0 −1 0 0 0 0 0 0

1 0 1 0

0

0 0

0

0 1 0 0 0 0

0 0⎤ 0 0 ⎥⎥ 0 0 0⎥ ⎥ 0 0 0⎥ 0 0 0⎥ ⎥ 1 0 1⎥ 0 1 0⎥ ⎥ −1 0 1 ⎦⎥ 0 0

5 ⎡1 ⎢0 ⎢ ⎢0 ⎢ 0 M=⎢ ⎢0 ⎢ ⎢0 ⎢0 ⎢ ⎢⎣ 0 ⎡1 1 ⎢1 −1 ⎢ ⎢0 0 ⎢ 0 0 A1 = ⎢ ⎢0 0 ⎢ ⎢0 0 ⎢0 0 ⎢ ⎣⎢0 0

0 0 0 1 0 0 0 0.7071 0 0 0 1 0 0 0 0

0 0 0 0

0 0 0 0

0⎤ 0 ⎥⎥ 0⎥ ⎥ 0⎥ 0 −0.9239 −0.3827 0 ⎥ ⎥ 0 0.7071 0 0⎥ 0 0.9239 0 ⎥ −0.3827 ⎥ 0 0 0 1 ⎥⎦ 0 0 0 0

0 0 0 0 0 0⎤ ⎡1 0 0 1 0 0 ⎢0 1 1 0 0 0 0 0 0 0 0 0 ⎥⎥ ⎢ 1 1 0 0 0 0⎥ ⎢0 1 −1 0 0 0 ⎥ ⎢ 0 1 0 0 0 0⎥ ⎢0 0 0 −1 0 0 = A 2 ⎢0 0 0 0 −1 −1 0 0 1 0 0 0⎥ ⎥ ⎢ 0 0 0 1 0 0⎥ ⎢0 0 0 0 0 1 ⎢0 0 0 0 0 0 0 0 0 0 1 0⎥ ⎥ ⎢ 0 0 0 0 0 1 ⎦⎥ ⎣⎢0 0 0 0 0 0

0 0 0 0

0 0⎤ 0 0 ⎥⎥ 0 0⎥ ⎥ 0 0⎥ 0 0⎥ ⎥ 1 0⎥ 1 1⎥ ⎥ 0 1 ⎦⎥

0 0 0 0

⎡1 ⎢0 ⎢ ⎢0 ⎢ 0 A3 = ⎢ ⎢0 ⎢ ⎢0 ⎢0 ⎢ ⎢⎣1

0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0

1⎤ 0 ⎥⎥ 0 1 0 0⎥ ⎥ 1 0 0 0⎥ −1 0 0 0 ⎥ ⎥ 0 −1 0 0 ⎥ 0 0 −1 0 ⎥ ⎥ 0 0 0 −1⎥⎦ 0 0

0 0

0 1

Through processing all the coefficient blocks using (1), the service provider generates the down-sampled DCT coefficients. After quantizing all the 8×8 blocks of these coefficients with the table QT, he generates a rescaled JPEG image by entropy encoding. 2.3 Decryption of the Rescaled Image On the recipient side, after receiving the encryption keys and parameters (K1, K2, K3, T, R) from the image owner, content of the rescaled image can be decrypted. Using entropy decoding, the recipient first decodes the rescaled JPEG image into quantized DCT coefficients F(i, j), where i=1, 2, …, M/2 and j=1, 2, …, N/2, and divides F into MN/64 non-overlapped 8×8 blocks. With the encryption key K3, the recipient reorders the permuted coefficient blocks in F to F'. With the keys and parameters (K1, K2, T, R), the recipient reconstructs the mask MS using the same algorithm in Sub-section 2.1. Down-sample MS using (1) to generate MS', a mask (M/2)×(N/2) integers. Then, he decrypts the encrypted coefficients into DE by DE=F'–MS' Finally, the recipient encodes DE into a decrypted JPEG file using entropy encoding again. Thus, the plaintext JPEG image sized (M/2)×(N/2) is generated.

3. Experimental Results and Discussion The grayscale image sized 512×384 in Fig. 2(a) is from the UCID database [21]. We compressed the image by JPEG using the quality factor 80. Fig. 2(b) is the encrypted JPEG image, in which the details and the structure of the content are encrypted. Parameters used here are T=6 and R=10. Fig. 2(c) is the JPEG image rescaled by the 5

6 service provider, and Fig. 2(d) the rescaled image by decrypting Fig. 2(c) using the keys and parameters. Both Fig. 2(c) and (d) are sized 256×192. Fig. 3(d) shows that the resulting plaintext image has a good visual quality. To evaluate the rescaled image on the recipient side, we rescale the original JPEG image using “bicubic” interpolation to generate the reference image, and compare the rescaled image with the reference. Fig. 3 shows the Peak Signal-to-Noise Ratio (PSNR) values of the rescaled images after decryption corresponding to different parameters. It should be noted that T=1 corresponds to the case that only DC coefficients are encrypted. Different quality factors of JPEG compression are also used. Fig. 3(a) and (c) are the results of “Lena” compressed by quality factors 80 and 50 respectively, and Fig. 3(b) and (d) the results of “Baboon” using quality factors 80 and 50 respectively. All the results illustrate that the rescaled images have good quality. When T or R is larger, there is less information leakage of the original image, while the quality of the rescaled images is asymptotically depressed. For a better evaluation, we arbitrarily use 200 images from the UCID database to implement the proposed method. Different parameters for T and R, and the quality factors 50 and 80 are used. The average PSNR values of the decrypted images are presented in Table I, which shows that the proposed method has a good rescaling capability. Although the JPEG file length is be enlarged as encryption changes the details and the structure of the original image, the rescaling reduces the data amount to large extent. Table II and Table III shows the experimental results of the file sizes of encrypted image and the rescaled image before decryption, in which the original images “Lena” and “Baboon” are used. The original JPEG file lengths of “Lena” and “Baboon” are 37937KB and 78687KB, respectively. Compared with the original, file lengths of the encrypted images increase 6% to 80% corresponding to different parameters. After rescaling the encrypted image, file sizes of the encrypted images decrease 40% to 66%. As to the cipher security, we use three steps to encrypt the original content of the JPEG images. We first encrypt the DC coefficients by adding pseudo-randomly generated integer sequence uniformly distributed on [–128,128]. There are totally 257MN/64 possible sequences. Then, L AC coefficients on T sub-bands are encrypted by adding pseudo-randomly generated another integer sequence uniformly distributed on [–R, R]. Thus, there are totally (2R+1)L possible sequences. The marked image is then disordered by block shuffling, and the possibility equals (MN/256)!. As long as M, N and T are not too small, it would be impossible for an eavesdropper to successively break the original content by exhaustive searching.

4. Conclusions

6

7 The proposed protocol shows that the JPEG image can be encrypted for privacy protection and rescaled in the encrypted domain to reduce the image size. This protocol ensures that the texture and the structure of the JPEG image are encrypted. Combined with the encryption algorithm, down-sampling the encrypted DCT coefficient is feasible. The rescaled image can be decrypted on the recipient side to construct a plaintext image with a lower resolution. With the proposed method, data amount of the encrypted JPEG image can be reduced after image rescaling, and the rescaled image can be preserved with good quality. Since this method can rescale the image to 1/4 of the original, smaller rescaling ratios, i.e. 1/4n (n≥2), can also be achieved. To realize the capability of generating arbitrarily rescaled image is the goal of our future work.

Acknowledgements This work was supported by Shanghai Rising-Star Program under Grant 14QA1401900, the Natural Science Foundation of China under Grant 61103181, Grant 61202367 and Grant 61472235, the Natural Science Foundation of Shanghai under Grant 12ZR1443700 and Grant 14ZR1415100, and the Innovation Program of Shanghai Municipal Education Commission under Grant 14YZ020.

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[2]

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[3]

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[4]

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[5]

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[6]

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[7]

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[8]

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[9]

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8 2010. [10] M. Johnson, P. Ishwar, V. M. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process., vol. 52, no. 10, pp. 2992–3006, Oct. 2004. [11] W. Liu, W. Zeng, L. Dong, and Q. Yao, “Efficient compression of encrypted grayscale images,” IEEE Trans. Image Process., vol. 19, no. 4, pp. 1097–1102, Apr. 2010. [12] X. Zhang, “Lossy compression and iterative reconstruction for encrypted image,” IEEE Trans. Inform. Forensics Security, vol. 6, no. 1, pp. 53–58, Feb. 2011. [13] X. Zhang, G. Feng, Y. Ren and Z. Qian, “Scalable Coding of Encrypted Images,” IEEE Trans. Inform. Forensics Security, vol. 21, no. 6, pp.3108-3114, June 2012. [14] X. Zhang, “Reversible data hiding in encrypted images,” IEEE Signal Process. Lett., vol. 18, no. 4, pp. 255–258, Apr. 2011. [15] W. Hong, T. Chen, and H. Wu, “An improved reversible data hiding in encrypted images using side match,” IEEE Signal Process. Lett., vol. 19, no. 4, pp. 199–202, Apr. 2012. [16] X. Zhang, “Separable reversible data hiding in encrypted image,” IEEE Trans. Inf. Forensics Security, vol. 7, no. 2, pp. 826–832, Apr. 2012. [17] K. Ma, W. Zhang, et al. “Reversible Data Hiding in Encrypted Images by Reserving Room Before Encryption,” IEEE Trans. Inf. Forensics Security, vol. 8, no. 3, 553-562, 2013. [18] Z. Qian, X. Zhang and S. Wang, “Reversible Data Hiding in Encrypted JPEG Bitstream,” IEEE Trans. on Multimedia, vol. 16, no. 5, pp. 1486-1491, 2014. [19] R. L. Lagendijk, Z. Erkin, M. Barni. “Encrypted signal processing for privacy protection: Conveying the utility of homomorphic encryption and multiparty computation,” IEEE Trans. Signal Processing Magazine, vol. 30, no.1, pp. 82-105, 2013. [20] N. Merhav and V. Bhaskaran. “Fast algorithms for DCT-domain image downsampling and for inverse motion compensation,” IEEE Trans. Circuits and Systems for Video Technology, vol. 7, no. 3, pp. 468-476, 1997.

[21] G. Schaefer and M. Stich, “UCID: An Uncompressed Colour Image Database,” in Proc. SPIE: Storage and Retrieval Methods and Applications for Multimedia, vol. 5307, pp. 472–480, 2004.

8

9

JPEG file

Entropy Decoding

K1, K2

K3

Cipher Mask Generation

Rescaled JPEG file (encrypted) Entropy Encoding

Entropy Decoding

Coefficient Quantization

Cipher Mask Generation

Resizing Calculation

Mask Resizing

Inverse Quantization

Coefficient Decryption

Entropy Decoding

Entropy Encoding

K1, K2

Coefficient Encryption

Entropy Encoding

Encrypted JPEG file Image Owner

Rescaled JPEG file Service Provider Fig. 1 Sketch of the proposed protocol

9

Recipient

K3

10

(a)

(b)

(c)

(d)

Fig. 2 Rescaling the Privacy-Protected Image, (a) is the original image, (b) the encrypted image, (c) the rescaled encrypted image, (d) the rescaled image after decryption

10

11

35

PSNR

34 33

29

32

28

31 1 2 3 4 5 6 7 8 9 1011121314 15 T

27 1 2 3 4 5 6 7 8 9 1011121314 15 T

(a)

(b)

31

26

29 28

R=2 R=5 R=10 R=15 R=20

25 PSNR

R=2 R=5 R=10 R=15 R=20

30 PSNR

R=2 R=5 R=10 R=15 R=20

30 PSNR

R=2 R=5 R=10 R=15 R=20

24 23

27 26 1 2 3 4 5 6 7 8 9 1011121314 15 T

22 1 2 3 4 5 6 7 8 9 1011121314 15 T

(c)

(d)

Fig. 3 Quality of the rescaled images corresponding to different parameters T, R, and quality factor QF, (a) “Lena” with quality factor QF=80, and (b) “Baboon” with quality factor QF=80, (c) “Lena” with quality factor QF=50, and (b) “Baboon” with quality factor QF=50

11

12

Table I Average PSNR values (dB) of the rescaled images set using different parameters and quality factors Quality Factor

T

R=2

R=5

R=10

R=15

R=20

T=2

28.7

28.6

28.6

28.5

28.5

T=3

28.6

28.5

28.2

28.0

27.9

T=4

28.5

27.8

27.4

27.1

26.6

T=5

28.3

27.1

26.4

26.1

25.9

T=2

33.1

33.1

33.1

33.0

33.0

T=3

33.1

33.0

32.8

32.6

32.5

T=4

32.9

32.5

32.2

31.9

31.6

T=5

32.8

32.0

31.4

31.1

30.9

QF=50

QF=80

12

13

Table II File lengths (KB) of the encrypted images and the rescaled images before decryption using the image “Lena” R=2

R=5

R=10

R=15

R=20

40189,

40557,

41261,

41841,

42375,

23766

23708

23814

24118

24414

40757,

42195,

44434,

46056,

47665,

23709

23758

24423

25336

26382

42282,

45575,

50253,

53450,

56643,

23742

24127

25684

27386

29119

45411,

51426,

59441,

64640,

69919,

23799

24762

27313

29755

31947

T=2

T=3

T=4

T=5

13

14

Table III File lengths (KB) of the encrypted images and the rescaled images before decryption using the image “Baboon” R=2

R=5

R=10

R=15

R=20

80724,

80817,

81138,

81488,

81830,

26881

26890

27015

27201

27431

80832,

81304,

82369,

83505,

84654,

26882

27020

27449

28060

28818

81027,

82284,

84900,

87354,

89757,

26944

27249

28294

29549

30880

81641,

84438,

89577,

93904,

98079,

27051

27714

29452

31264

32938

T=2

T=3

T=4

T=5

14

15

Highlights · · · ·

The JPEG encryption protocol is suitable for image rescaling in encrypted domain. Privacy of the original image can be preserved when transmitted to the server. The encrypted JPEG image can be rescaled by the service provider. On the recipient side, the rescaled image can be decrypted with good quality.

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