A Similarity Search Scheme over Encrypted Cloud Images based on Secure Transformation

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1 A Simiarity Search Scheme over Encrypted Coud Images based on Secure Transormation Zhihua Xia, Yi Zhu, Xingming Sun, and Jin Wang Jiangsu Engineering Center o Network Monitoring, Nanjing University o Inormation Science & Technoogy, Nanjing, 0044, China Schoo o Computer & Sotware, Nanjing University o Inormation Science & Technoogy, Nanjing, 0044, China Abstract. With the growing popuarity o coud computing, more and more users outsource their private data to the coud. To ensure the security o private data, data owners usuay encrypt their private data beore outsourcing the data to the coud server, which brings incommodity o data operating. This paper proposes a scheme or simiar search on encrypted images based on a secure transormation method. The transormation on eatures protects the inormation about eatures, and does not degrade the resut accuracy. Moreover, the image owner coud update the encrypted image database as we as the secure index very easiy. Introduction Due to strong data storage and management abiity o the coud server, more and more data owners wi outsource data to the coud server. In order to ensure the security o private data, data owners need to encrypt their data beore upoading the data. Unortunatey, data encryption, i not done appropriatey, may reduce the eectiveness o data utiization. For exampe, content-based image retrieva (CBIR) techniue has been widey used in the rea word; however, the technoogies are invaid ater the eature vectors are encrypted. Currenty, searchabe symmetric encryption has been widey researched. Song et a. proposed the irst practica searchabe encryption method []. Ater that, in order to enhance the search exibiity and usabiity, some researchers proposed works to support simiar keyword search which coud toerate typing errors [-4]. On the other hand, some o the works ocused on muti-keyword searches which coud return more accurate resuts ranked according to some predeined criterions [5-8]. However, these works are mainy designed or the search on encrypted texts, and coud not be utiized directy or the encrypted images. Inspired by the searchabe encryption on texts, Lu et a. proposed a search scheme over encrypted mutimedia databases [9]. They extracted visua words rom images, based on which they coud achieve simiar search on encrypted images with the methods that are usuay empoyed by the encrypted text search schemes. However, this work is not suitabe or other image eatures except the NGCIT 03, ASTL Vo. 7, pp , 03 SERSC 03 03

2 Proceedings, The nd Internationa Conerence on Next Generation Computer and Inormation Technoogy visua words, and their index makes the search resut ess accurate. In this paper, we propose a scheme that not ony ensure the security o the images and eatures but aso support simiar search on encrypted images. In the proposed scheme, the encryption on eatures does not degrade the resut accuracy. Moreover, the image owner coud update the encrypted image database as we as the secure index uite easiy. Probem Formuations The proposed scheme incudes three dierent entities: image owner, coud server, and image user. Image owner has a coection o n images M = { m, m,, m n } that he wants to outsource to the coud server in encrypted orm. Meanwhie, the image owner wants to keep the capabiity to search through the images or eective utiization reasons. First, the image owner extracts a eature vector = (,,, ) T rom each image as common image retrieva system does. Secondy, the images are encrypted. Thirdy, the image owner buids a secure searchabe index I with the set{ } n i i=. Finay, the encrypted images and the index I are upoaded to the coud server. Image user is the authorized ones to use the images. We assume that the authorization between the image owner and image user is appropriatey done. In order to uery images, the image user extracts the uery eature vector rom the uery image. Then, the vector is used to generate a trapdoor TD( ). Finay, the trapdoor TD( ) is submitted to the coud server or the purpose o searching simiar images. Coud server stores the encrypted images and the index I or the image owner and processes the uery o image users. Ater receiving a uery trapdoor TD( ), coud server compares the trapdoor T ( ) with the items in index I to return k most simiar images. 3 Preiminaries 3. Feature Extraction Content-based image retrieva usuay invoves extraction o eatures and search on the eature index or simiar images. Without oss o generaity, the proposed scheme chooses the histogram eatures which are the most typica and simpest ones or CBIR. 04

3 A Simiarity Search Scheme over Encrypted Coud Images based on Secure Transormation We denote mxas ( ) the gray vaue at the ocation x in an image m. Then, the histogram eatures can be ormuated as { mx ( ) = i} i =, () m where { mx ( ) = i} =, i mxeuas ( ) to i, ese { mx ( ) = i} =0, m is the pixe number o the image. The simiarity between two histogram eature vectors can be evauated by Eucidean distance, deined as ( ),, D(, )= =. () i j i j ik jk k = 3. Secure Transormation Approach Image eatures in paintext may revea inormation about image content. First, the eature vector = (,,, ) T is extended as where = i i= an ( + ) ( + ) invertibe matrix R as T = (,,, ), (3). Then, the modiied eature vector is transormed with T = R, (4) where the matrix R is kept as the secure key by image owner and the authorized image user. In summary, the secure transorm agorithm can be written as = SecureTransrom( R, ) T T = R (,...,, ). (5) 4 The Proposed Scheme To achieve secure simiar search on images outsourced to the coud, the image owner needs to construct a secure searchabe index and outsource it to the coud server aong with the encrypted images. Ater that, coud server coud perorm simiar search on the index according to the uery reuests submitted by image users. The proposed scheme needs to ensure that the coud server earns nothing about the uery, index, and image databases. In this section, we describe our scheme in detai in two phases. 05

4 Proceedings, The nd Internationa Conerence on Next Generation Computer and Inormation Technoogy 4. The Setup Phase In the setup phase, image owner needs to buid a secure index and encrypt the images. Then, the index and the encrypted images are upoaded to the coud. Step: Key Generation. The image owner generates the private key k img eature vectors respectivey. Step: Feature Extraction. and R to encrypt the images and the The image owner extracts a eature vector = (,,, ) T rom each image in the databases M. In the proposed scheme, the eatures are the histogram eatures as it is described in subsection 3.. Step3: Secure Index Construction. Ater the eature vectors are extracted rom the image database M, they are utiized to buid secure searchabe index I. The image owner transorms each with private key R by using the secure transormation method SecureTransrom( R, ) so as to generate the corresponding encrypted eature vector. Then, the secure index I is constructed as shown in Tabe, where ID( m i ) is the identiier o ie mi that can uniuey ocate the actua ie. Tabe. The secure searchabe index I ID( m ) ID( m ) ID( m ) 3 3 ID( m ) n n Step4: Upoad. Ater constructing the index I, data owner encrypts a o the images in M with the secure key k img. Then, the encrypted images and the secure searchabe index I are upoaded to the coud. 06

5 A Simiarity Search Scheme over Encrypted Coud Images based on Secure Transormation 4. Search phase In search phase, the image user wants to retrieve images that are simiar to a uery image rom the coud server. In order to avoid the inormation eakage, the image user generates a secure trapdoor with the uery image. Then, the trapdoor is submitted to the coud server. Utiizing the trapdoor, the coud server returns k most simiar images by searching on the index I. Step: Trapdoor Generation. In order to uery images, the image user extracts the uery eature vector = (,,...,, ) rom the uery image with the eature extraction method introduced in the step o setup phase. Then, the uery eature vector is used to generate a trapdoor TD( ) as oowing. First, with the, the image user generates = (,...,,) T. (6),, Then, the trapdoor TD( ) is cacuated as TD R, (7) ( ) = r where r is a positive random rea number, and R is the shared secure key. Finay, the trapdoor TD( ) is submitted to coud server by the image user. Step: Search Index. Ater receiving a search reuest TD( ), the coud server wi search on the secure index I, and return k most simiar images to the user. The distance between uery vector and the vector i, i =,..., n, can be cacuated as oows: Dis TD T ( ( ), i) = ( TD( )) i T T T T ( rr (,,...,,,) ) ( R ( i,,..., i,, i ) ) = T T T,, R R i, i, i = r(,...,,) ( ) (,...,, ) ( i ) = r. (8) For every uery, the r and between and i is impied in the are the same or every i, and the Eucidean distance ( ( ), i) Dis TD. Thereore, with this distance criterion, the coud server coud return the same k most simiar resuts exacty as it does on unencrypted eature vectors. Finay, the coud server returns k most simiar resuts with minimum distance to the uery vector to image user, who coud decrypt the images with the shared key k img. 07

6 Proceedings, The nd Internationa Conerence on Next Generation Computer and Inormation Technoogy 5 Security and Perormance 5. Security Anaysis () Conidentiaity o the data: In the proposed scheme, the image database, index, and uery are encrypted. The coud server can not access the origina images and eature vectors without the secure key k img and R. () Query uninkabiity: By introducing the random vaue r in trapdoor generation, the same uery reuests wi generate dierent trapdoors. Thus, uery uninkabiity is better protected. 5. Perormance () Resut accuracy: This criterion is used to evauate the correction o the returned resuts. The accuracy o the scheme is mainy decided by the eature extraction method in common image retrieva systems. The proposed scheme hods the same resut accuracy as the common schemes that do not encrypt the eature vectors according to the ormua (8). () Time compexity: The process o index construction incudes eature extraction and eature vector transormation. The time cost o cacuation o histogram is O ( m n). Here, m is pixe number o the image, and n is number o images. The transormation o eature vectors invoves a mutipication o a ( + ) ( + ) matrix, and thus, the time cost iso (( + ) n). In summary, the time compexity o index construction iso (( m + ( + ) ) n). The search process incudes trapdoor generation and search, the time costs o which areo( ) and O ( n), respectivey. In summary, the time compexities o index construction and uery are determined by the size o database n. 6 Concusion A basic simiarity search scheme over encrypted images is proposed based on a secure transormation approach. The proposed scheme protects the conidentiaity o image database, eature vectors, and user s uery. Meanwhie, the proposed scheme possesses the same accuracy as the schemes which use the same eature extraction method but do not encrypt the eatures. However, the proposed scheme is by no means the optima one. It does not bedim the search pattern and access pattern, and thus may suer rom statistic attacks. In addition, the time compexity o uery on invert index is O ( n), which can be urther improved by using better index. In uture, we wi improve our scheme in these two aspects. 08

7 A Simiarity Search Scheme over Encrypted Coud Images based on Secure Transormation Acknowedgements. This work is supported by the NSFC (6306, 6034, , , 6734, 6734, 67336, 6035, 63733, , and 60739), Nationa Basic Research Program 973 (0CB3808), 0GK009, GYHY006033, , 03DFG860, SBC030569, Research Start-Up und o NUIST (0048), and PAPD und. Reerences. D. X. Song, et a., "Practica techniues or searches on encrypted data," in Security and Privacy, 000. S&P 000. Proceedings. 000 IEEE Symposium on, ed: IEEE, 000, pp C. Wang, et a., "Achieving usabe and privacy-assured simiarity search over outsourced coud data," in INFOCOM, 0 Proceedings IEEE, pp , J. Li, et a., "Fuzzy keyword search over encrypted data in coud computing," in INFOCOM, 00 Proceedings IEEE, pp. -5, M. Chuah and W. Hu, "Privacy-aware bedtree based soution or uzzy muti-keyword search over encrypted data," in Distributed Computing Systems Workshops (ICDCSW), 0 3st Internationa Conerence on, pp. 73-8, D. Boneh and B. Waters, "Conjunctive, subset, and range ueries on encrypted data," in Theory o cryptography, ed: Springer, 007, pp C. Ning, et a., "Privacy-preserving muti-keyword ranked search over encrypted coud data," in INFOCOM, 0 Proceedings IEEE, pp , W. Sun, et a., "Privacy-preserving muti-keyword text search in the coud supporting simiarity-based ranking," in Proceedings o the 8th ACM SIGSAC symposium on Inormation, computer and communications security, pp. 7-8, X. Jun, et a., "Two-Step-Ranking Secure Muti-Keyword Search over Encrypted Coud Data," in Coud and Service Computing (CSC), 0 Internationa Conerence on, pp. 4-30, W. Lu, et a., "Enabing search over encrypted mutimedia databases," in IS&T/SPIE Eectronic Imaging, pp ,

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