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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 01 | Jan -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 634
Review on Key Based Encryption Scheme for Secure Data Sharing on
Cloud
Miss. Swati V.Thakre1, Prof. K.K.Chhajed2, Prof.V.B.Bhagat3
1Miss.Swati V.Thakre, P.R.Pote College Of Engineering, Maharashtra, India.
2 Prof. K. K. Chhajed, Assistant Professor Department of Computer Science and Engineering,
P.R.Pote College Of Engineering, Maharashtra, India.
3Prof. V. B. Bhagat, Assistant Professor Department of Computer Science and Engineering,
P.R.Patil College Of Engineering, Maharashtra, India.
---------------------------------------------------------------------***----------------------------------------------------------------------
Abstract: Cloud technology isveryconstructiveanduseful
in present new technological era. Cloudcomputinghasgiven
the users the accessibility to deploy number of files to the
centralized cloud and share those with number of users.
Cloud computing always comes with the hurdles of security
concerns. Hence to achieve cloud data security, To enable
secure and flexible data sharing in the cloud, efficient
management of encryption keys are required .The data
owner always needs to encrypt the files before uploading
and it must decrypt before end users. This system needs
secure storage of keys, but as files gets increased in number
keys management becomes complex. By using Key based
Encryption scheme user only need to submit aggregate key
for file sharing in groups and searchableencryptionand also
submit aggregate trapdoor. This system provide number of
benefits to multiuser and also reduce trapdoor.
Key Word: Searchable Encryption, Cloud Computing,
Aggregate Key, Data Privacy
1. INTRODUCTION
Cloud architecture can be used to allow data
sharing capabilities and this can provide n number of
benefits to the user. At present there is a push for IT
organizations to increase their data sharing efforts. Cloud
computing, also known as 'on-demand computing', is a
kind of Internet-basedcomputing,wheresharedresources,
data and information are provided to computersandother
devices on-demand [2]. There are some requirements in
cloud system for sharing data securely. First, the data
owner should be able to specify a set of users that are
permitted to view data. Any member within the group
should be able to gain access to the data anytime. The data
owner should be able to add new users, revoke access
rights against any member of the group over his or her
shared data. Data owner or groupadmin,whenhewantsto
share his data in the group he sends a key to the members
of the group for data encryption [3]. And users get the
access to the data with the help of any member of the
group can then get the encrypted data from the cloud and
decrypt the data using the key. But still this technique will
not work properly if there is n number of users in the
group.
While considering data privacy, we cannot relyon
traditional technique of authentication, because
unexpected privilege escalation will expose all data.
Solution is to encrypt data before uploading to the server
with users own key. Data sharing is again important
functionality of cloud storage, because user can share data
from anywhere and anytime to anyone. So our aim is to
develop an efficient data sharing scheme that enable
complete control. This scheme also aimstoenablegroup of
users perform a keyword search over authorized
encrypted files using single aggregate trapdoor generated
from the single aggregate key [4].
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 01 | Jan -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 635
2. AIM
To provide data storage and better data sharing in
cloud, ensuring data security is important.Dailymillionsof
user shares their data on cloud. A misbehaving cloud
operator can pose seriousthreatofdata stealing.Generally,
key based encryption is used for ensuring data security.
3. LITERATURE SURVEY
Achieving Secure, Scalable, and Fine-Grained Data
Access Control in Cloud Computing
Author: S. Yu, C. Wang, K. Ren, and W. Lou,
In [1], Yu et al. presented a scalable and fine-grained data
access control scheme incloudcomputingbasedontheKP-
ABE technique. In this paper the data ownerusesa random
key to encrypt a file, where the random key is further
encrypted with a set of attributes using KP-ABE. Then, the
group manager assigns an access structure and the
corresponding secret key to authorized users, such that a
user can only decrypt a cipher text if and only if the data
file attributes satisfy the access structure. To achieve user
revocation, the manager delegate’s tasks of data file re
encryption and user secret key update to cloud servers.
However, the single-owner manner may hinder the
implementation of applications with the scenario, where
any member in a group should be allowed to store and
share data files with others.
Multi Key Searchable Encryption
Author: Raluca Ada Popa and Nickolai Zeldovich
Popa [2] firstly introduces the concept of multi-key
searchable encryption (MKSE). In this scheme documents
encrypted with different keys. Such scheme called asmulti
key search .This scheme hides the content of thedocument
and the words one searches for, and the only information
the server learns is whether some word beingsearchedfor
matches a word in a document. It also provides data
confidentiality in client-server applications againstattacks
on the server. The most challenging aspect when coming
up with such a scheme is that there is no single trusted
user.
Multi User Searchable Encryption
Author: R. Curtmola, J. Garay, S. Kamara, R. Ostrovsky.
In this paper curtmola introduced rich literature on
searchable encryption, including SSE schemes [3] and
PEKS schemes [4]. In contrast to thoseexistingwork,inthe
context of cloud storage, keyword search under the multi-
tenancy setting is a more common scenario. In such a
scenario, the data owner would like to share a document
with a group of authorized users, and each user who has
the access right can provide a trapdoor to perform the
keyword search over the share a document witha groupof
authorized users, and each user who has the access right
can provide a trapdoor to perform the keyword search
over the shared document, namely, the “multi-user
searchable encryption” (MUSE) scenario.
Secure Multi Owner Data Sharing for Dynamic Groups
in the Cloud
AUTHORS: Xuefeng Liu, Yuqing Zhang
Xuefeng Liu et al. [5] proposed a secure multi-owner data
sharing scheme, named Mona. It implies that any user in
the group can securely share data with others by the
untrusted cloud. The proposed scheme is able to support
dynamic groups efficiently. Specifically, newgrantedusers
can directly decrypt data files uploaded before their
participation without contacting with data owners. User
revocation can be easily achieved through a novel
revocation list without updating the secret keys of the
remaining users. The size and computation overhead of
encryption are constant and independentwiththenumber
of revoked users. This scheme provides secure and
privacy-preserving access control to users, which
guarantees any member in a group to anonymously utilize
the cloud resource.
Key-Aggregate CryptosystemforScalableDataSharing
in Cloud Storage
Author: Cheng-Kang Chu, Sherman S. M. Chow, Wen-Guey
Tzeng, Jianying Zhou
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 01 | Jan -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 636
Cheng-Kang Chu et al. [6] introduce a public-key
encryption scheme called as key-aggregate cryptosystem
(KAC) to securely, efficiently, and flexibly share data with
others in cloud storage. In KAC, users encrypt a message
not only under a public-key, but also under an identifier of
cipher text called class. That means the cipher texts are
further categorized into different classes. The key owner
holds a master-secret key, which can be used to extract
secret keys for different classes. The extracted key have
can be an aggregate key which is as compactasa secretkey
for a single class, but aggregates the power of many such
keys, i.e., the decryption power for any subset of cipher
text classes. In KAC the sizes of cipher text, public-key,
master-secret key, and aggregate key are all of constant
size.
3.1 Limitation of Existing System
Existing solutions are difficult to detect faults in Web
applications deployed in a large scale dynamic cloud
computing environment due to the following reasons:
1. Data leaks in the cloud.
2. The costs and complexities involved generally
increase with the number of the decryption keys
to be shared.
3. The encryption key and decryption key are
different in public key encryption.
4. Large number of keys for both encryption and
search.
5. Large number of trapdoor must be generated by
the user and submitted to the cloud in order to
perform a keyword search over many files.
6. The implied need for secure communication,
storage, and complexity clearly renders the
approach impractical.
4. PROPOSED SYSTEM
The capability of selectively sharing encrypted data with
different users via public cloud storage may greatly ease.
Any group of selected document shared with group of
user’s demands different encryption key to be used for
different documents.so large number of key uses for both
encryption and search .and also submit large number of
trapdoor to the cloud in order to perform search data over
shared document. This leads to key management and
storage problem. This practical problem can be addressed
by using Key Based Encryption scheme.
System play main three role user which is
uploaded files and cloud service provider, third one is
admin .user registered and added in group if group of user
want to share files then encrypted before uploaded to
cloud then aggregate key send to another group of user
only authenticate user can decrypt files group of manager
provide key to group of user then usercanaccessfilesfrom
cloud, search keyword using single trapdoor. System
composed of seven polynomial algorithms for security.
Parameter setup, key generation, encryption, key
extraction, trapdoor generation, trapdoor adjustment,and
trapdoor testing.
1. Setup: The cloud server will use this algorithm to
initialize system parameters.
2. Keygen: Data owner uses this algorithm to
generate his/her key pair.
3. Encrypt: Data owner uses this algorithm to
encrypt data and generate its keyword cipher
texts when uploading the i-th document.
4. Extract: Data owner uses this algorithm to
generate an aggregate searchable encryption key.
5. Trapdoor: The user uses this algorithm to
generate the trapdoorto performkeywordsearch.
6. Adjust: The cloud server uses this algorithm to
produce the right trapdoor.
7. Test: The cloud server uses this algorithm to
perform keyword search over the i-th document.
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 01 | Jan -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 637
Figure 1: Framework of system
5. CONCLUSION
Key based encryption Scheme can provide an effective
solution for secure and scalable data sharing systembased
on the cloud storage. In Key based encryption scheme, the
owner only needs to distribute a single key to a user when
sharing lots of documents with the user, and the user only
needs to submit a single trapdoor when he queries overall
documents shared by the same owner. Federated clouds
are getting popular nowadays, but proposed scheme
cannot be directly applied. So it is also a future scope to
apply this scheme in the federated cloud environment.
REFERENCES
[1] S. Yu, C. Wang, K. Ren, and W. Lou, “Achieving Secure,
Scalable, and Fine-Grained Data Access Control in Cloud
Computing”,Proc. IEEE INFOCOM, pp. 534-542, 2010.
2] R. A. Popa ,N. Zeldovich. “Multi-key searchable
encryption”.Cryptology ePrint Archive, Report 2013/508,
2013.Computing”,Proc.ACMSymp.Information,Computer
and Comm. Security, pp. 282-292, 2010.
[3] X. Song, D. Wagner, A. Perrig. “Practical techniques for
searches on encrypted data”, IEEE Symposium on Security
and Privacy, IEEE Press, pp. 44C55, 2000.
[4] R. Curtmola, J. Garay, S. Kamara, R. Ostrovsky.
“Searchable symmetric encryption: improved definitions
and efficient constructions”, In: Proceedings of the 13th
ACM conference on Computer and Communications
Security, ACM Press, pp. 79-88, 2006.
[5] X. Liu, Y. Zhang, B. Wang, and J. Yan. “Mona: secure
multiowner data sharing for dynamic groups in the cloud”,
IEEE Transactions on Parallel and Distributed Systems,
2013, 24(6): 1182-1191.
[6] C. Chu, S. Chow,W. Tzeng, et al. “Key-Aggregate
Cryptosystem for Scalable Data Sharing in Cloud Storage”,
IEEE Transactions on Parallel and Distributed Systems,
2014, 25(2): 468-477.
[7] P. Van,S. Sedghi,JM.Doumen.“Computationallyefficient
searchable symmetric encryption”, Secure Data
Management, pp.87-100, 2010.
[8] S. Kamara, C. Papamanthou, T. Roeder. “Dynamic
searchable symmetric encryption”, Proceedings of the
2012 ACM conferenceon Computer and communications
security (CCS), ACM, pp. 965-976, 2012.
[9] D. Boneh, C. G, R. Ostrovsky, G. Persiano. “Public Key
Encryption with Keyword Search”, EUROCRYPT 2004, pp.
506C522, 2004.
[10] Y. Hwang, P. Lee. “Public Key Encryption with
Conjunctive Keyword Search and Its Extension to a Multi-
user System”, In: Pairing-Based Cryptography C Pairing
2007, LNCS, pp. 2-22, 2007.

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Key Based Encryption Scheme for Secure Cloud Data Sharing

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 01 | Jan -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 634 Review on Key Based Encryption Scheme for Secure Data Sharing on Cloud Miss. Swati V.Thakre1, Prof. K.K.Chhajed2, Prof.V.B.Bhagat3 1Miss.Swati V.Thakre, P.R.Pote College Of Engineering, Maharashtra, India. 2 Prof. K. K. Chhajed, Assistant Professor Department of Computer Science and Engineering, P.R.Pote College Of Engineering, Maharashtra, India. 3Prof. V. B. Bhagat, Assistant Professor Department of Computer Science and Engineering, P.R.Patil College Of Engineering, Maharashtra, India. ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract: Cloud technology isveryconstructiveanduseful in present new technological era. Cloudcomputinghasgiven the users the accessibility to deploy number of files to the centralized cloud and share those with number of users. Cloud computing always comes with the hurdles of security concerns. Hence to achieve cloud data security, To enable secure and flexible data sharing in the cloud, efficient management of encryption keys are required .The data owner always needs to encrypt the files before uploading and it must decrypt before end users. This system needs secure storage of keys, but as files gets increased in number keys management becomes complex. By using Key based Encryption scheme user only need to submit aggregate key for file sharing in groups and searchableencryptionand also submit aggregate trapdoor. This system provide number of benefits to multiuser and also reduce trapdoor. Key Word: Searchable Encryption, Cloud Computing, Aggregate Key, Data Privacy 1. INTRODUCTION Cloud architecture can be used to allow data sharing capabilities and this can provide n number of benefits to the user. At present there is a push for IT organizations to increase their data sharing efforts. Cloud computing, also known as 'on-demand computing', is a kind of Internet-basedcomputing,wheresharedresources, data and information are provided to computersandother devices on-demand [2]. There are some requirements in cloud system for sharing data securely. First, the data owner should be able to specify a set of users that are permitted to view data. Any member within the group should be able to gain access to the data anytime. The data owner should be able to add new users, revoke access rights against any member of the group over his or her shared data. Data owner or groupadmin,whenhewantsto share his data in the group he sends a key to the members of the group for data encryption [3]. And users get the access to the data with the help of any member of the group can then get the encrypted data from the cloud and decrypt the data using the key. But still this technique will not work properly if there is n number of users in the group. While considering data privacy, we cannot relyon traditional technique of authentication, because unexpected privilege escalation will expose all data. Solution is to encrypt data before uploading to the server with users own key. Data sharing is again important functionality of cloud storage, because user can share data from anywhere and anytime to anyone. So our aim is to develop an efficient data sharing scheme that enable complete control. This scheme also aimstoenablegroup of users perform a keyword search over authorized encrypted files using single aggregate trapdoor generated from the single aggregate key [4].
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 01 | Jan -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 635 2. AIM To provide data storage and better data sharing in cloud, ensuring data security is important.Dailymillionsof user shares their data on cloud. A misbehaving cloud operator can pose seriousthreatofdata stealing.Generally, key based encryption is used for ensuring data security. 3. LITERATURE SURVEY Achieving Secure, Scalable, and Fine-Grained Data Access Control in Cloud Computing Author: S. Yu, C. Wang, K. Ren, and W. Lou, In [1], Yu et al. presented a scalable and fine-grained data access control scheme incloudcomputingbasedontheKP- ABE technique. In this paper the data ownerusesa random key to encrypt a file, where the random key is further encrypted with a set of attributes using KP-ABE. Then, the group manager assigns an access structure and the corresponding secret key to authorized users, such that a user can only decrypt a cipher text if and only if the data file attributes satisfy the access structure. To achieve user revocation, the manager delegate’s tasks of data file re encryption and user secret key update to cloud servers. However, the single-owner manner may hinder the implementation of applications with the scenario, where any member in a group should be allowed to store and share data files with others. Multi Key Searchable Encryption Author: Raluca Ada Popa and Nickolai Zeldovich Popa [2] firstly introduces the concept of multi-key searchable encryption (MKSE). In this scheme documents encrypted with different keys. Such scheme called asmulti key search .This scheme hides the content of thedocument and the words one searches for, and the only information the server learns is whether some word beingsearchedfor matches a word in a document. It also provides data confidentiality in client-server applications againstattacks on the server. The most challenging aspect when coming up with such a scheme is that there is no single trusted user. Multi User Searchable Encryption Author: R. Curtmola, J. Garay, S. Kamara, R. Ostrovsky. In this paper curtmola introduced rich literature on searchable encryption, including SSE schemes [3] and PEKS schemes [4]. In contrast to thoseexistingwork,inthe context of cloud storage, keyword search under the multi- tenancy setting is a more common scenario. In such a scenario, the data owner would like to share a document with a group of authorized users, and each user who has the access right can provide a trapdoor to perform the keyword search over the share a document witha groupof authorized users, and each user who has the access right can provide a trapdoor to perform the keyword search over the shared document, namely, the “multi-user searchable encryption” (MUSE) scenario. Secure Multi Owner Data Sharing for Dynamic Groups in the Cloud AUTHORS: Xuefeng Liu, Yuqing Zhang Xuefeng Liu et al. [5] proposed a secure multi-owner data sharing scheme, named Mona. It implies that any user in the group can securely share data with others by the untrusted cloud. The proposed scheme is able to support dynamic groups efficiently. Specifically, newgrantedusers can directly decrypt data files uploaded before their participation without contacting with data owners. User revocation can be easily achieved through a novel revocation list without updating the secret keys of the remaining users. The size and computation overhead of encryption are constant and independentwiththenumber of revoked users. This scheme provides secure and privacy-preserving access control to users, which guarantees any member in a group to anonymously utilize the cloud resource. Key-Aggregate CryptosystemforScalableDataSharing in Cloud Storage Author: Cheng-Kang Chu, Sherman S. M. Chow, Wen-Guey Tzeng, Jianying Zhou
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 01 | Jan -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 636 Cheng-Kang Chu et al. [6] introduce a public-key encryption scheme called as key-aggregate cryptosystem (KAC) to securely, efficiently, and flexibly share data with others in cloud storage. In KAC, users encrypt a message not only under a public-key, but also under an identifier of cipher text called class. That means the cipher texts are further categorized into different classes. The key owner holds a master-secret key, which can be used to extract secret keys for different classes. The extracted key have can be an aggregate key which is as compactasa secretkey for a single class, but aggregates the power of many such keys, i.e., the decryption power for any subset of cipher text classes. In KAC the sizes of cipher text, public-key, master-secret key, and aggregate key are all of constant size. 3.1 Limitation of Existing System Existing solutions are difficult to detect faults in Web applications deployed in a large scale dynamic cloud computing environment due to the following reasons: 1. Data leaks in the cloud. 2. The costs and complexities involved generally increase with the number of the decryption keys to be shared. 3. The encryption key and decryption key are different in public key encryption. 4. Large number of keys for both encryption and search. 5. Large number of trapdoor must be generated by the user and submitted to the cloud in order to perform a keyword search over many files. 6. The implied need for secure communication, storage, and complexity clearly renders the approach impractical. 4. PROPOSED SYSTEM The capability of selectively sharing encrypted data with different users via public cloud storage may greatly ease. Any group of selected document shared with group of user’s demands different encryption key to be used for different documents.so large number of key uses for both encryption and search .and also submit large number of trapdoor to the cloud in order to perform search data over shared document. This leads to key management and storage problem. This practical problem can be addressed by using Key Based Encryption scheme. System play main three role user which is uploaded files and cloud service provider, third one is admin .user registered and added in group if group of user want to share files then encrypted before uploaded to cloud then aggregate key send to another group of user only authenticate user can decrypt files group of manager provide key to group of user then usercanaccessfilesfrom cloud, search keyword using single trapdoor. System composed of seven polynomial algorithms for security. Parameter setup, key generation, encryption, key extraction, trapdoor generation, trapdoor adjustment,and trapdoor testing. 1. Setup: The cloud server will use this algorithm to initialize system parameters. 2. Keygen: Data owner uses this algorithm to generate his/her key pair. 3. Encrypt: Data owner uses this algorithm to encrypt data and generate its keyword cipher texts when uploading the i-th document. 4. Extract: Data owner uses this algorithm to generate an aggregate searchable encryption key. 5. Trapdoor: The user uses this algorithm to generate the trapdoorto performkeywordsearch. 6. Adjust: The cloud server uses this algorithm to produce the right trapdoor. 7. Test: The cloud server uses this algorithm to perform keyword search over the i-th document.
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 01 | Jan -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 637 Figure 1: Framework of system 5. CONCLUSION Key based encryption Scheme can provide an effective solution for secure and scalable data sharing systembased on the cloud storage. In Key based encryption scheme, the owner only needs to distribute a single key to a user when sharing lots of documents with the user, and the user only needs to submit a single trapdoor when he queries overall documents shared by the same owner. Federated clouds are getting popular nowadays, but proposed scheme cannot be directly applied. So it is also a future scope to apply this scheme in the federated cloud environment. REFERENCES [1] S. Yu, C. Wang, K. Ren, and W. Lou, “Achieving Secure, Scalable, and Fine-Grained Data Access Control in Cloud Computing”,Proc. IEEE INFOCOM, pp. 534-542, 2010. 2] R. A. Popa ,N. Zeldovich. “Multi-key searchable encryption”.Cryptology ePrint Archive, Report 2013/508, 2013.Computing”,Proc.ACMSymp.Information,Computer and Comm. Security, pp. 282-292, 2010. [3] X. Song, D. Wagner, A. Perrig. “Practical techniques for searches on encrypted data”, IEEE Symposium on Security and Privacy, IEEE Press, pp. 44C55, 2000. [4] R. Curtmola, J. Garay, S. Kamara, R. Ostrovsky. “Searchable symmetric encryption: improved definitions and efficient constructions”, In: Proceedings of the 13th ACM conference on Computer and Communications Security, ACM Press, pp. 79-88, 2006. [5] X. Liu, Y. Zhang, B. Wang, and J. Yan. “Mona: secure multiowner data sharing for dynamic groups in the cloud”, IEEE Transactions on Parallel and Distributed Systems, 2013, 24(6): 1182-1191. [6] C. Chu, S. Chow,W. Tzeng, et al. “Key-Aggregate Cryptosystem for Scalable Data Sharing in Cloud Storage”, IEEE Transactions on Parallel and Distributed Systems, 2014, 25(2): 468-477. [7] P. Van,S. Sedghi,JM.Doumen.“Computationallyefficient searchable symmetric encryption”, Secure Data Management, pp.87-100, 2010. [8] S. Kamara, C. Papamanthou, T. Roeder. “Dynamic searchable symmetric encryption”, Proceedings of the 2012 ACM conferenceon Computer and communications security (CCS), ACM, pp. 965-976, 2012. [9] D. Boneh, C. G, R. Ostrovsky, G. Persiano. “Public Key Encryption with Keyword Search”, EUROCRYPT 2004, pp. 506C522, 2004. [10] Y. Hwang, P. Lee. “Public Key Encryption with Conjunctive Keyword Search and Its Extension to a Multi- user System”, In: Pairing-Based Cryptography C Pairing 2007, LNCS, pp. 2-22, 2007.