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Fully Secure Multi-authority Ciphertext-Policy Attribute-Based Encryption without Random Oracles Zhen Liu1,2 1 Shanghai Jiao Tong University, Shanghai, China 2 City University of Hong Kong, Hong Kong SAR, China Joint work with Zhenfu Cao, Qiong Huang, Duncan S. Wong, and Tsz Hon Yuen 16th European Symposium on Research in Computer Security (ESORICS) 2011, 12-14 September 2011, Leuven, Belgium Outline Introduction History Motivation Our Results Background Our scheme 2 Introduction: What is CP-ABE? CP-ABE is a tool for implementing fine-grained access control over encrypted data, and is conceptually similar to traditional access control methods such as Role-Based Access Control. A user is described by a set of descriptive attributes, and a corresponding private key is issued to the user by an authority. During encryption, an encryptor associates an access policy over attributes with the ciphertext. If and only if the attributes of a user satisfy the access policy of the ciphertext, the user can decrypt the ciphertext . 3 Introduction: What is CP-ABE? , , … ℎ , , … , , … 1980, 1981 , … …… ….. Dept.: CS, EE, … Type: PhD Stud., Alumni, … Gender: Male, Female Birth Year: 1980, 1981, … …… …… = (, , ) satisfies = {, ℎ} M Storage Server (Untrusted) AND = {, ℎ} OR CS PDH ALUMNI = (ℎ ) does not satisfy 4 Introduction: What is CP-ABE? -- Collusion-resistant If none of the users can decrypt a ciphertext individually, they still can’t even if they work together. = {, ℎ} AND OR CS PDH ALUMNI = (ℎ ) = {, } 5 Introduction: What is CP-ABE? -- Definition • • • • , ⟶ , . , , ⟶ . is implicitly included in . (, , ) ⟶ . , , ⟶ ⊥. If and only if satisfies , can be recovered. 6 Introduction: Why needs MA-CP-ABE? It might not be realistic to have one single authority to manage all attributes. [SW05] E.g., an encryptor may want to share data with users who are computer science alumni of University X and currently working as an engineer for Company Y. i.e., the access policy is = . . . In a desired Multi-Authority CP-ABE (MA-CP-ABE) system, different domains of attributes are managed by different authorities. An encryptor can encrypt messages with any access policy over the entire attribute universe. 7 History: Existing CP-ABE Schemes Goyal et al. [GPSW06]: CP-ABE notion. Bethencourt, Sahai and Waters [BSW07] : The first CP-ABE scheme. Cheung and Newport [CN07] are proposed to Goyal et al. [GJPS08] achieve better and Waters [Waters08/11] better expressiveness, Lewko et al.[LOSTW10] Okamoto and Takashima[OT10] efficiency and security. [Waters08/11] and [LOSTW10]: expressive (any monotone access structure); efficient; and secure. The two constructions are very similar, and the difference is that [Waters08/11] is on prime order group while [LOSTW10] is on composite order group. [Waters08/11] is selectively secure and [LOSTW10] is adaptively secure. 8 History: Existing MA-CP-ABE Schemes Müller et al. [MKE09]: One Central Authority (CA) and Multiple Attribute Authorities (AAs). • Selectively secure. • Key Escrow: The CA can decrypt all ciphertexts. Lewko and Waters [LW11] : Multiple AAs • The AAs operate independently from each other. • Adaptively secure, in the random oracle model. • Key Escrow: Each AA can decrypt the ciphertexts whose policy can be satisfied by the AA’s attribute domain. 9 Motivation Construct an MA-CP-ABE system Different attribute domains are managed by different authorities. Expressiveness, efficiency and security are not weaker than that of the single-authority CP-ABE in [LOSTW10]: Expressiveness: Support any monotone access structure over the entire attribute universe; Efficiency: similar to that of [LOSTW10]; Security: adaptively secure in the standard model. No authority can independently decrypt any ciphertext. 10 Our Results We constructed a new MA-CP-ABE system. Multiple CAs and Multiple AAs. The CAs issue identity-related keys to users but do not involve in any attribute-related operations. The AAs issue attribute-related keys to users. Each AA manages a different attribute domain, and operates independently from other AAs. A party may easily join the system as an AA by registering itself to the CAs and publishing its attribute-related parameters. The expressiveness, efficiency and security are comparable to that of the single-authority CP-ABE scheme in [LOSTW10]. No authority can independently decrypt any ciphertext. 11 Our Results LOSTW10 (SA-) CP-ABE LW11 MA-CP-ABE Ours MA-CP-ABE Standard Model Multi-Authority Prevent Decryption by Individual Authority Partially Size of Ciphertext + + + Size of Secret key + || + ( + ) + || + + || ++ Pairing Computation of Decryption Size of Public key : The number of CAs. : The number of AAs. 12 The rest of this presentation… 1. Bilinear map and access structure 2. Our construction 3. Extensions 13 Background Bilinear map: = 1 2 3 where 1 , 2 and 3 are three distinct primes; and are cyclic groups of order ; : × → is a map such that (1) Bilinear: ∀ , ℎ ∈ , , ∈ , e g a , hb = e g, h ab ; (2) Non-Degenerate: ∃ ∈ , such that (, ) has order in . LSSS: Any monotone access structure can be realized by a Linear SecretShare Scheme (LSSS). An LSSS is a labeled matrix (, ), where is a × matrix over ∗ and labels each row with a share holder. E.g., (2,2) 1 1 1 1 1 2 1 1 3 (2,3) D 1 2 0 A B C 14 Our MA-CP-ABE Scheme: Idea Start from the single authority CP-ABE of [LOSTW10]: , → , . : , , ℎ, , , = ∀ ∈ ; : , 3 , ℎ ∈ 1 , ∈ are chosen randomly, 3 is a generator of 3 . , , → = (, , ∀ ∈ ). = ℎ 0 , = 0′ , = ∀ ∈ . ∈ , 0 , 0′ , ∈ 3 are chosen randomly. , , , → . = ⋅ , , ′ = ℎ , = ℎ ⋅ − , ′ = ∀ ∈ {1,2 … , }. , ∈ are chosen randomly. , , → . ⋅ ∈ Constants { } satisfy , ′ , ′, ∈ = (1,0, … , 0). = . 15 Our MA-CP-ABE Scheme: Idea , , → = (, , ∀ ∈ ). = ℎ 0 , = 0′ , = ∀ ∈ . ∈ , 0 , 0′ , ∈ 3 are chosen randomly. Have no relation with attributes Bind all attribute-related keys of a user together; Prevent collusion attack from different users (Distinct random for each user); = = = /0′ ′ = Ideas: Separate the single authority to one CA and multiple AAs CA is responsible for choosing and generating for users; When a user submits his to an AA, the AA generates by using . Problem: is submitted to AA by the user, so that two users (e.g., Bob and Tom) can launch a collusion attack by submitting the same . Solution: Use digit signature to bind and the identity of a user together. 16 Our MA-CP-ABE Scheme: Idea One-CA-Multi-AA → , . : , , ℎ, , , = ∀ ∈ , 3 , ; : , , → , . : , , ℎ, , , = ∀ ∈ ; : ∀ ∈ → (, , ∀ ∈ ). = ℎ 0 , = 0′ , = ∀ ∈ . = (, || ) , , → . = ℎ 0 , = 0′ , = , , , , → . = ⋅ , , ′ = ℎ , = ℎ ⋅ − , ′ = ∀ ∈ {1,2 … , }. 17 Our MA-CP-ABE Scheme: Idea One-CA-Multi-AA Problem: Multi-CA-Multi-AA In the One-CA-Multi-AA system, the CA holds the value of , so that it can decrypt all ciphertexts. Solution Introduce multiple CAs: CA1, …, CAD . Each CAd chooses independently, and publishes , to the public parameters. In algorithm, = ⋅ , . Implicitly, we have set that = 1 + 2 + ⋯ + . Only when all CAs collude together, can they decrypt a ciphertext. 18 1 …… 1 1 User = {1 , 2 } 1 ∈ 1 , 2 ∈ …… Our MA-CP-ABE Scheme: Idea Naive Multi-CA-Multi-AA → : , , ℎ, 3 → : , , ; : , , → : = ∀ ∈ ; : ∀ ∈ , → (, , , ). , = ℎ, 0 , , = , 0′ , , = ( , || d|| , ) {, , , | = 1,2, … , }, → {,, }. ,, = , ,, , = 1,2, … , , , → . =⋅ , , ′ = ℎ , = ℎ ⋅ − , ′ = ∀ ∈ {1,2 … , }. , , → . ∈ =1 , , ′ , ,, ′ , , = =1 1 , . 20 Our MA-CP-ABE Scheme: Idea Naive Multi-CA-Multi-AA Our MA-CP-ABE Problem: When an attacker corrupts a CA, collusion attack can be launched. E.g., = 2, = 2. 1 ∈ 1 , 2 ∈ 2 . = 1 , = {2 }. CA1 is corrupted by Bob and Tom, while CA2 is still secure. In such a case, Bob and Tom should not be able to decrypt a ciphertext with policy (1 2 ). However, Bob obtains ,2 , ,2 from CA2 ; then obtains 1,,2 from AA1 ; They set ,1 = ,2 , and submit this ,1 to AA2 . AA2 is cheated and believes that this “ ,1 " is legal, because Bob and Tom control CA1 so that they can generate the valid signature. Then AA2 generates "2 ,,1 " by using this " ,1 ", which is actually "2 ,,2 " for ",2 “. For the ciphertext, they can reconstruct , 2 by using ,2 , ,2 , {1,,2 , 2,,2 }. --- COLLUSION ATTACK WORKS. 21 Our MA-CP-ABE Scheme: Idea Our MA-CP-ABE Naive Multi-CA-Multi-AA Solution: Each time CAd generates , = , ′, it must show the knowledge of , to AAk . We addressed this by reusing the CP-ABE scheme of [LOSTW10]. 1 When visits , regards as the “attributes” of the user User 1 = { 1,1 , 2,1 , … , (, 1)} 2 = 1,2 , 2,2 , … , , 2 = { 1, , 2, , … , (, )} 2 registers , to ; uses , as the public key corresponding to “attribute (k,d)” , = , 1,1 = 1,1 1,2 = 1,2 2,1 = 2,1 2,2 = 2,2 1 2 1,1 , 1,2 2,1 , 2,2 22 Our MA-CP-ABE Scheme: Idea Our MA-CP-ABE Naive Multi-CA-Multi-AA [LOSTW10] , , → = (, , ∀ ∈ ) . = ℎ 0 , = 0′ , = ∀ ∈ . When visits , regards = { 1, , 2, , … (, )} as the “attributes” of the user: , takes the place of [Ours] , → (, , , , Γ,, = 1 ). , = ℎ, 0 , , = , 0′ , Γ,, = , , ( = 1 ), , = ( , || || || Γ,,1 || … ||Γ,, ) . uses Γgid,d,k to show to that the corresponding , is generated honestly. 23 Conclusion We constructed an MA-CP-ABE system, where Different domains of attributes are managed by different attribute authorities, which operate independently from each other. No authority can independently decrypt any ciphertext. LOSTW10 (SA-) CP-ABE LW10 MA-CP-ABE Ours MA-CP-ABE Standard Model Multi-Authority Prevent Decryption by Individual Authority Partially Size of Ciphertext + + + Size of Secret key + || + ( + ) + || + + || ++ Pairing Computation of Decryption Size of Public key 24 Extensions Large attribute universe construction: The size of public key is linear in ||. It can be avoided by using the idea of interpolation. Improving performance and reliability of the system: In this paper, = 1 + 2 + ⋯ + is used to distribute to CAs. It is a (, )-threshold policy, so that all CAs must remain active. In the full version of this paper, general , Δ -threshold policy is used. Only when CAs are involved, they can decrypt a ciphetext. The system works as long as no more than Δ − D CAs fail. 25 References • [SW05] Sahai, A., Waters, B.: Fuzzy identity-based encryption. EUROCRYPT 2005. • [GPSW06] Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for finegrained access control of encrypted data. ACM CCS 2006. • [BSW07] Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attributebased encryption. IEEE Symposium on Security and Privacy, 2007 • [CN07] Cheung, L., Newport, C.C.: Provably secure ciphertext policy abe. ACM CCS 2007 • [GJPS08] Goyal, V., Jain, A., Pandey, O., Sahai, A.: Bounded Ciphertext Policy Attribute Based Encryption. ICALP 2008, Part II. • [Waters08/11] Waters, B.: Ciphertext-policy attribute-based encryption: An expressive, efficient, and provably secure realization. PKC 2011 • [LOSTW10]Lewko, A.B., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: Attribute-based encryption and (Hierarchical) inner product encryption. EUROCRYPT 2010. 26 Reference • [OT10] Okamoto, T., Takashima, K. : Fully secure functional encryption with general relations from the decisional linear assumption. CRYPTO 2010. • [MKE09] M¨uller, S., Katzenbeisser, S., Eckert, C.: On multi-authority ciphetext-policy attribute-based encryption. Bulletin of the Korean Mathematical Society 2009. • [LW11] Lewko, A., Waters, B.: Decentralizing attribute-based encryption. EUROCRYPT 2011. 27 Thanks. Q&A 28