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#13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6.
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CONTROL CLOUD DATA ACCESS PRIVILEGE AND ANONYMITY WITH FULLY
ANONYMOUS ATTRIBUTE-BASED ENCRYPTION.
ABSTRACT
Cloud computing is a revolutionary computing paradigm, which enables flexible, on-
demand, and low-cost usage of computing resources, but the data is outsourced to some cloud
servers, and various privacy concerns emerge from it. Various schemes based on the attribute-
based encryption have been proposed to secure the cloud storage. However, most work focuses
on the data contents privacy and the access control, while less attention is paid to the privilege
control and the identity privacy. In this paper, we present a semi anonymous privilege control
scheme Annoy Control to address not only the data privacy, but also the user identity privacy in
existing access control schemes. Annoy Control decentralizes the central authority to limit the
identity leakage and thus achieves semi anonymity. Besides, it also generalizes the file access
control to the privilege control, by which privileges of all operations on the cloud data can be
managed in a fine-grained manner. Subsequently, we present the Annoy Control-F, which fully
prevents the identity leakage and achieve the full anonymity. Our security analysis shows that
both Annoy Control and Annoy Control-F are secure under the decisional bilinear Differ–
Hellman assumption, and our performance evaluation exhibits the feasibility of our schemes.
#13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6.
Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602,
Project Titles: http://shakastech.weebly.com/2015-2016-titles
Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com
EXISTING SYSTEM:
A multi-authority system is presented in which each user has an ID and they can interact
with each key generator (authority) using different pseudonyms. One user’s different
pseudonyms are tied to his private key, but key generators never know about the private keys,
and thus they are not able to link multiple pseudonyms belonging to the same user. Also, the
whole attributes set is divided into N disjoint sets and managed by N attributes authorities. In this
setting, each authority knows only a part of any user’s attributes, which are not enough to figure
out the user’s identity. However, the scheme proposed by Chase et al. considered the basic
threshold-based KP-ABE, which lacks generality in the encryption policy expression. Many
attribute based encryption schemes having multiple authorities have been proposed afterwards,
but they either also employ a threshold-based ABE, or have a semi-honest central authority, or
cannot tolerate arbitrarily many users’ collusion attack. The work by Lewko et al. And Muller et
al. are the most similar ones to ours in that they also tried to decentralize the central authority in
the CP-ABE into multiple ones. Lewko et al. use a LSSS matrix as an access structure, but their
scheme only converts the AND, OR gates to the LSSS matrix, which limits their encryption
policy to Boolean formula, while we inherit the flexibility of the access tree having threshold
gates. Muller et al. also supports only Disjunctive Normal Form (DNF) in their encryption
policy. Besides the fact that we can express arbitrarily general encryption policy, our system also
tolerates the compromise attack towards attributes authorities, which is not covered in many
existing works.
#13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6.
Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602,
Project Titles: http://shakastech.weebly.com/2015-2016-titles
Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com
PROPOSED SYSTEM:
Therefore, we propose Anony Control and AnonyControl-F (Fig. 1) to allow cloud
servers to control users’ access privileges without knowing their identity information. Their main
merits are:
1) The proposed schemes are able to protect user’s privacy against each single authority. Partial
information is disclosed in AnonyControl and no information is disclosed in AnonyControl-F.
2) The proposed schemes are tolerant against authority compromise, and compromising of up to
(N −2) authorities does not bring the whole system down.
3) We provide detailed analysis on security and performance to show feasibility of the scheme
AnonyControl and AnonyControl-F.
4) We firstly implement the real toolkit of a multiauthority based encryption scheme
AnonyControl and AnonyControl-F.
Module 1
System Model
In our system, there are four types of entities: N Attribute Authorities (denoted as A),
Cloud Server, Data Owners and Data Consumers. A user can be a Data Owner and a Data
Consumer simultaneously. Authorities are assumed to have powerful computation abilities, and
they are supervised by government offices because some attributes partially contain users’
personally identifiable information. The whole attribute set is divided into N disjoint sets and
controlled by each authority, therefore each authority is aware of only part of attributes. A Data
Owner is the entity who wishes to outsource encrypted data file to the Cloud Servers. The Cloud
Server, who is assumed to have adequate storage capacity, does nothing but store them. Newly
joined Data Consumers request private keys from all of the authorities, and they do not know
which attributes are controlled by which authorities. When the Data Consumers request their
private keys from the authorities, authorities jointly create corresponding private key and send it
to them. All Data Consumers are able to download any of the encrypted data files, but only those
whose private keys satisfy the privilege tree Tp can execute the operation associated with
#13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6.
Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602,
Project Titles: http://shakastech.weebly.com/2015-2016-titles
Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com
privilege p. The server is delegated to execute an operation p if and only if the user’s credentials
are verified through the privilege tree Tp
Module 2
DesignGoals
Our goal is to achieve a multi-authority CP-ABE which: achieves the security defined
above; guarantees the confidentiality of Data Consumers’ identity information; and tolerates
compromise attacks on the authorities or the collusion attacks by the authorities. For the visual
comfort, we frequently use the following notations hereafter. Ak denotes the k-th attribute
authority; Au denotes the attributes set of user u; Auk denotes the subset of Au controlled by Ak;
and ATp denotes the attributes set included in tree Tp.
Module 3
Anon control construction
Setup At the system initialization phase, any one of the authorities chooses a bilinear
group G0 of prime order p with generator g and publishes it. Then, all authorities independently
and randomly picks vk ∈ Zp and send Yk = e(g, g)vk to all there authorities who individually
compute Y := _k∈A Yk = e(g, g)_k∈A vk . Then, every authority Ak randomly picks N − 1
integers skj ∈ Zp( j ∈ {1, . . . , N}{k}) and computes gskj . Each gskj is shared with each other
authority Aj. An authority Ak, after receiving N −1 pieces of gs jk generated by Aj.
Module 4
#13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6.
Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602,
Project Titles: http://shakastech.weebly.com/2015-2016-titles
Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com
ACHIEVING FULL ANONYMITY
We have assumed semi-honest authorities in AnonyControl and we assumed that they
will not collude with each ther. This is a necessary assumption in AnonyControl because each
authority is in charge of a subset of the whole attributes set, and for the attributes that it is in
charge of, it knows the exact information of the key requester. If the information from all
authorities is gathered altogether, the complete attribute set of the key requester is recovered and
thus his identity is disclosed to the authorities. In this sense, AnonyControl is semi anonymous
since partial identity information (represented as some attributes) is disclosed to each authority,
but we can achieve a full-anonymity and also allow the collusion of the authorities. The key
point of the identity information leakage we had in our previous scheme as well as every existing
attribute based encryption schemes is that key generator (or attribute authorities in our scheme)
issues attribute key based on the reported attribute, and the generator has to know the user’s
attribute to do so. We need to introduce a new technique to let key generators issue the correct
attribute key without knowing what attributes the users have. A naive solution is to give all the
attribute keys of all the attributes to the key requester and let him pick whatever he wants. In this
way, the key generator does not know which attribute keys the key requester picked, but we have
to fully trust the key requester that he will not pick any attribute key not allowed to him. To solve
this, we leverage the following Oblivious Transfer (OT).
Module 5
Fully Anonymous Multi-Authority CP-ABE
In this section, we present how to achieve the full anonymity in AnonyControl to designs
the fully anonymous privilege control scheme AnonyControl-F. The Key Generate algorithm is
the only part which leaks identity information to each attribute authority. Upon receiving the
attribute key request with the attribute value, the attribute authority will generate H(att (i ))ri and
sends it to the requester where att (i ) is the attribute value and ri is a random number for that
#13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6.
Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602,
Project Titles: http://shakastech.weebly.com/2015-2016-titles
Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com
attribute. The attribute value is disclosed to the authority in this step. We can introduce the above
1-out-of-n OT to prevent this leakage. We let each authority be in charge of all attributes
belonging to the same category. For each attribute category c (e.g., University), suppose there are
k possible attribute values (e.g., IIT, NYU, CMU ...), then one requester has at most one attribute
value in one category. Upon the key request, the attribute authority can pick a random number ru
for the requester and generates H(att (i ))ru for all i ∈ {1, . . . , k}. After the attribute keys are
ready, the attribute authority and the key requester are engaged in a 1-out-of-k OT where the key
requester wants to receive one attribute key among k. By introducing the 1-out-of-k OT in our
Key Generate algorithm, the key requester achieves the correct attribute key that he wants, but
the attribute authority does not have any useful information about what attribute is achieved by
the requester. Then, the key requester achieves the full anonymity in our scheme and no matter
how many attribute authorities collude; his identity information is kept secret.
CONCLUSION AND POSSIBLE EXTENSIONS
This paper proposes a semi-anonymous attribute-based privilege control scheme
AnonyControl and a fully-anonymous attribute-based privilege control scheme AnonyControl-F
to address the user privacy problem in a cloud storage server. Using multiple authorities in the
cloud computing system, our proposed schemes achieve not only fine-grained privilege control
but also identity anonymity while conducting privilege control based on users’ identity
information. More importantly, our system can tolerate up to N − 2 authority compromise, which
is highly preferable especially in Internet-based cloud computing environment. We also
conducted detailed security and performance analysis which shows that Anony- Control both
secure and efficient for cloud storage system. The AnonyControl-F directly inherits the security
of the AnonyControl and thus is equivalently secure as it, but extra communication overhead is
incurred during the 1-out-of-n oblivious transfer. One of the promising future works is to
introduce the efficient user revocation mechanism on top of our anonymous ABE. Supporting
user revocation is an important issue in the real application, and this is a great challenge in the
#13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6.
Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602,
Project Titles: http://shakastech.weebly.com/2015-2016-titles
Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com
application of ABE schemes. Making our schemes compatible with existing ABE schemes that
support efficient user revocation is one of our future works.
REFERENCES
[1] A. Shamir, “Identity-based cryptosystems and signature schemes,” in Advances in
Cryptology. Berlin, Germany: Springer-Verlag, 1985, pp. 47–53.
[2] A. Sahai and B. Waters, “Fuzzy identity-based encryption,” in Advances in Cryptology.
Berlin, Germany: Springer-Verlag, 2005, pp. 457–473.
[3] V. Goyal, O. Pandey, A. Sahai, and B. Waters, “Attribute-based encryption for fine-grained
access control of encrypted data,” in Proc. 13th CCS, 2006, pp. 89–98.
[4] J. Bettencourt, A. Sahai, and B. Waters, “Cipher text-policy attribute based encryption,” in
Proc. IEEE SP, May 2007, pp. 321–334.
[5] M. Chase, “Multi-authority attribute based encryption,” in Theory of Cryptography. Berlin,
Germany: Springer-Verlag, 2007, pp. 515–534.
[6] M. Chase and S. S. M. Chow, “Improving privacy and security in multi-authority attribute-
based encryption,” in Proc. 16th CCS, 2009, pp. 121–130.
[7] H. Lin, Z. Cao, X. Liang, and J. Shao, “Secure threshold multi authority attribute based
encryption without a central authority,” Inf. Sci., vol. 180, no. 13, pp. 2618–2632, 2010.
[8] V. Božovi´c, D. Socked, R. Steinwandt, and V. I. Villányi, “Multi-authority attribute-based
encryption with honest-but-curious central authority,” Int. J. Comput. Math., vol. 89, no. 3, pp.
268–283, 2012.
[9] F. Li, Y. Rahulamathavan, M. Rajarajan, and R. C.-W. Phan, “Low complexity multi-
authority attribute based encryption scheme for mobile cloud computing,” in Proc. IEEE 7th
SOSE, Mar. 2013, pp. 573–577.
[10] K. Yang, X. Jia, K. Ren, and B. Zhang, “DAC-MACS: Effective data access control for
multi-authority cloud storage systems,” in Proc. IEEE INFOCOM, Apr. 2013, pp. 2895–2903

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Control cloud data access privilege and anonymity with fully anonymous attribute based encryption

  • 1. #13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6. Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602, Project Titles: http://shakastech.weebly.com/2015-2016-titles Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com CONTROL CLOUD DATA ACCESS PRIVILEGE AND ANONYMITY WITH FULLY ANONYMOUS ATTRIBUTE-BASED ENCRYPTION. ABSTRACT Cloud computing is a revolutionary computing paradigm, which enables flexible, on- demand, and low-cost usage of computing resources, but the data is outsourced to some cloud servers, and various privacy concerns emerge from it. Various schemes based on the attribute- based encryption have been proposed to secure the cloud storage. However, most work focuses on the data contents privacy and the access control, while less attention is paid to the privilege control and the identity privacy. In this paper, we present a semi anonymous privilege control scheme Annoy Control to address not only the data privacy, but also the user identity privacy in existing access control schemes. Annoy Control decentralizes the central authority to limit the identity leakage and thus achieves semi anonymity. Besides, it also generalizes the file access control to the privilege control, by which privileges of all operations on the cloud data can be managed in a fine-grained manner. Subsequently, we present the Annoy Control-F, which fully prevents the identity leakage and achieve the full anonymity. Our security analysis shows that both Annoy Control and Annoy Control-F are secure under the decisional bilinear Differ– Hellman assumption, and our performance evaluation exhibits the feasibility of our schemes.
  • 2. #13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6. Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602, Project Titles: http://shakastech.weebly.com/2015-2016-titles Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com EXISTING SYSTEM: A multi-authority system is presented in which each user has an ID and they can interact with each key generator (authority) using different pseudonyms. One user’s different pseudonyms are tied to his private key, but key generators never know about the private keys, and thus they are not able to link multiple pseudonyms belonging to the same user. Also, the whole attributes set is divided into N disjoint sets and managed by N attributes authorities. In this setting, each authority knows only a part of any user’s attributes, which are not enough to figure out the user’s identity. However, the scheme proposed by Chase et al. considered the basic threshold-based KP-ABE, which lacks generality in the encryption policy expression. Many attribute based encryption schemes having multiple authorities have been proposed afterwards, but they either also employ a threshold-based ABE, or have a semi-honest central authority, or cannot tolerate arbitrarily many users’ collusion attack. The work by Lewko et al. And Muller et al. are the most similar ones to ours in that they also tried to decentralize the central authority in the CP-ABE into multiple ones. Lewko et al. use a LSSS matrix as an access structure, but their scheme only converts the AND, OR gates to the LSSS matrix, which limits their encryption policy to Boolean formula, while we inherit the flexibility of the access tree having threshold gates. Muller et al. also supports only Disjunctive Normal Form (DNF) in their encryption policy. Besides the fact that we can express arbitrarily general encryption policy, our system also tolerates the compromise attack towards attributes authorities, which is not covered in many existing works.
  • 3. #13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6. Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602, Project Titles: http://shakastech.weebly.com/2015-2016-titles Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com PROPOSED SYSTEM: Therefore, we propose Anony Control and AnonyControl-F (Fig. 1) to allow cloud servers to control users’ access privileges without knowing their identity information. Their main merits are: 1) The proposed schemes are able to protect user’s privacy against each single authority. Partial information is disclosed in AnonyControl and no information is disclosed in AnonyControl-F. 2) The proposed schemes are tolerant against authority compromise, and compromising of up to (N −2) authorities does not bring the whole system down. 3) We provide detailed analysis on security and performance to show feasibility of the scheme AnonyControl and AnonyControl-F. 4) We firstly implement the real toolkit of a multiauthority based encryption scheme AnonyControl and AnonyControl-F. Module 1 System Model In our system, there are four types of entities: N Attribute Authorities (denoted as A), Cloud Server, Data Owners and Data Consumers. A user can be a Data Owner and a Data Consumer simultaneously. Authorities are assumed to have powerful computation abilities, and they are supervised by government offices because some attributes partially contain users’ personally identifiable information. The whole attribute set is divided into N disjoint sets and controlled by each authority, therefore each authority is aware of only part of attributes. A Data Owner is the entity who wishes to outsource encrypted data file to the Cloud Servers. The Cloud Server, who is assumed to have adequate storage capacity, does nothing but store them. Newly joined Data Consumers request private keys from all of the authorities, and they do not know which attributes are controlled by which authorities. When the Data Consumers request their private keys from the authorities, authorities jointly create corresponding private key and send it to them. All Data Consumers are able to download any of the encrypted data files, but only those whose private keys satisfy the privilege tree Tp can execute the operation associated with
  • 4. #13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6. Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602, Project Titles: http://shakastech.weebly.com/2015-2016-titles Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com privilege p. The server is delegated to execute an operation p if and only if the user’s credentials are verified through the privilege tree Tp Module 2 DesignGoals Our goal is to achieve a multi-authority CP-ABE which: achieves the security defined above; guarantees the confidentiality of Data Consumers’ identity information; and tolerates compromise attacks on the authorities or the collusion attacks by the authorities. For the visual comfort, we frequently use the following notations hereafter. Ak denotes the k-th attribute authority; Au denotes the attributes set of user u; Auk denotes the subset of Au controlled by Ak; and ATp denotes the attributes set included in tree Tp. Module 3 Anon control construction Setup At the system initialization phase, any one of the authorities chooses a bilinear group G0 of prime order p with generator g and publishes it. Then, all authorities independently and randomly picks vk ∈ Zp and send Yk = e(g, g)vk to all there authorities who individually compute Y := _k∈A Yk = e(g, g)_k∈A vk . Then, every authority Ak randomly picks N − 1 integers skj ∈ Zp( j ∈ {1, . . . , N}{k}) and computes gskj . Each gskj is shared with each other authority Aj. An authority Ak, after receiving N −1 pieces of gs jk generated by Aj. Module 4
  • 5. #13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6. Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602, Project Titles: http://shakastech.weebly.com/2015-2016-titles Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com ACHIEVING FULL ANONYMITY We have assumed semi-honest authorities in AnonyControl and we assumed that they will not collude with each ther. This is a necessary assumption in AnonyControl because each authority is in charge of a subset of the whole attributes set, and for the attributes that it is in charge of, it knows the exact information of the key requester. If the information from all authorities is gathered altogether, the complete attribute set of the key requester is recovered and thus his identity is disclosed to the authorities. In this sense, AnonyControl is semi anonymous since partial identity information (represented as some attributes) is disclosed to each authority, but we can achieve a full-anonymity and also allow the collusion of the authorities. The key point of the identity information leakage we had in our previous scheme as well as every existing attribute based encryption schemes is that key generator (or attribute authorities in our scheme) issues attribute key based on the reported attribute, and the generator has to know the user’s attribute to do so. We need to introduce a new technique to let key generators issue the correct attribute key without knowing what attributes the users have. A naive solution is to give all the attribute keys of all the attributes to the key requester and let him pick whatever he wants. In this way, the key generator does not know which attribute keys the key requester picked, but we have to fully trust the key requester that he will not pick any attribute key not allowed to him. To solve this, we leverage the following Oblivious Transfer (OT). Module 5 Fully Anonymous Multi-Authority CP-ABE In this section, we present how to achieve the full anonymity in AnonyControl to designs the fully anonymous privilege control scheme AnonyControl-F. The Key Generate algorithm is the only part which leaks identity information to each attribute authority. Upon receiving the attribute key request with the attribute value, the attribute authority will generate H(att (i ))ri and sends it to the requester where att (i ) is the attribute value and ri is a random number for that
  • 6. #13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6. Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602, Project Titles: http://shakastech.weebly.com/2015-2016-titles Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com attribute. The attribute value is disclosed to the authority in this step. We can introduce the above 1-out-of-n OT to prevent this leakage. We let each authority be in charge of all attributes belonging to the same category. For each attribute category c (e.g., University), suppose there are k possible attribute values (e.g., IIT, NYU, CMU ...), then one requester has at most one attribute value in one category. Upon the key request, the attribute authority can pick a random number ru for the requester and generates H(att (i ))ru for all i ∈ {1, . . . , k}. After the attribute keys are ready, the attribute authority and the key requester are engaged in a 1-out-of-k OT where the key requester wants to receive one attribute key among k. By introducing the 1-out-of-k OT in our Key Generate algorithm, the key requester achieves the correct attribute key that he wants, but the attribute authority does not have any useful information about what attribute is achieved by the requester. Then, the key requester achieves the full anonymity in our scheme and no matter how many attribute authorities collude; his identity information is kept secret. CONCLUSION AND POSSIBLE EXTENSIONS This paper proposes a semi-anonymous attribute-based privilege control scheme AnonyControl and a fully-anonymous attribute-based privilege control scheme AnonyControl-F to address the user privacy problem in a cloud storage server. Using multiple authorities in the cloud computing system, our proposed schemes achieve not only fine-grained privilege control but also identity anonymity while conducting privilege control based on users’ identity information. More importantly, our system can tolerate up to N − 2 authority compromise, which is highly preferable especially in Internet-based cloud computing environment. We also conducted detailed security and performance analysis which shows that Anony- Control both secure and efficient for cloud storage system. The AnonyControl-F directly inherits the security of the AnonyControl and thus is equivalently secure as it, but extra communication overhead is incurred during the 1-out-of-n oblivious transfer. One of the promising future works is to introduce the efficient user revocation mechanism on top of our anonymous ABE. Supporting user revocation is an important issue in the real application, and this is a great challenge in the
  • 7. #13/ 19, 1st Floor, Municipal Colony, Kangayanellore Road, Gandhi Nagar, vellore – 6. Off:0416-2247353 / 6066663 Mo: +91 9500218218 /8870603602, Project Titles: http://shakastech.weebly.com/2015-2016-titles Website:www.shakastech.com, Email - id:shakastech@gmail.com, info@shakastech.com application of ABE schemes. Making our schemes compatible with existing ABE schemes that support efficient user revocation is one of our future works. REFERENCES [1] A. Shamir, “Identity-based cryptosystems and signature schemes,” in Advances in Cryptology. Berlin, Germany: Springer-Verlag, 1985, pp. 47–53. [2] A. Sahai and B. Waters, “Fuzzy identity-based encryption,” in Advances in Cryptology. Berlin, Germany: Springer-Verlag, 2005, pp. 457–473. [3] V. Goyal, O. Pandey, A. Sahai, and B. Waters, “Attribute-based encryption for fine-grained access control of encrypted data,” in Proc. 13th CCS, 2006, pp. 89–98. [4] J. Bettencourt, A. Sahai, and B. Waters, “Cipher text-policy attribute based encryption,” in Proc. IEEE SP, May 2007, pp. 321–334. [5] M. Chase, “Multi-authority attribute based encryption,” in Theory of Cryptography. Berlin, Germany: Springer-Verlag, 2007, pp. 515–534. [6] M. Chase and S. S. M. Chow, “Improving privacy and security in multi-authority attribute- based encryption,” in Proc. 16th CCS, 2009, pp. 121–130. [7] H. Lin, Z. Cao, X. Liang, and J. Shao, “Secure threshold multi authority attribute based encryption without a central authority,” Inf. Sci., vol. 180, no. 13, pp. 2618–2632, 2010. [8] V. Božovi´c, D. Socked, R. Steinwandt, and V. I. Villányi, “Multi-authority attribute-based encryption with honest-but-curious central authority,” Int. J. Comput. Math., vol. 89, no. 3, pp. 268–283, 2012. [9] F. Li, Y. Rahulamathavan, M. Rajarajan, and R. C.-W. Phan, “Low complexity multi- authority attribute based encryption scheme for mobile cloud computing,” in Proc. IEEE 7th SOSE, Mar. 2013, pp. 573–577. [10] K. Yang, X. Jia, K. Ren, and B. Zhang, “DAC-MACS: Effective data access control for multi-authority cloud storage systems,” in Proc. IEEE INFOCOM, Apr. 2013, pp. 2895–2903