Fully Secure Multi-authority Ciphertext -Policy Attribute-Based Encryption without Random Oracles

1. Fully Secure Multi-authority Ciphertext-Policy Attribute-Based Encryption without Random Oracles Zhen Liu1,2 1 Shanghai Jiao Tong University, Shanghai, China 2City University of Hong Kong, Hong Kong SAR, China Joint work with ZhenfuCao, QiongHuang, Duncan S. Wong, and Tsz Hon Yuen 16th European Symposium on Research in Computer Security (ESORICS) 2011, 12-14 September 2011, Leuven, Belgium

2. Outline • Introduction • History • Motivation • Our Results • Background • Our scheme

3. 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 attributeswith the ciphertext. • If and only if the attributes of a user satisfy the access policy of the ciphertext, the user can decrypt the ciphertext .

4. Introduction: What is CP-ABE? Dept.: CS, EE, … Type: PhD Stud., Alumni, … Gender: Male, Female Birth Year: 1980, 1981, … …… …… , , … , , … , , … ,, … …… ….. satisfies M Storage Server (Untrusted) AND CS OR does not satisfy ALUMNI PDH

5. 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. AND CS OR ALUMNI PDH

6. Introduction: What is CP-ABE? -- Definition • . is implicitly included in . • . • If and only if satisfies , can be recovered.

7. 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.

8. 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] • Goyal et al. [GJPS08] • Waters [Waters08/11] • Lewko et al.[LOSTW10] • Okamoto and Takashima[OT10] are proposed to achieve better and better expressiveness, 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.

9. 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.

10. 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: adaptivelysecure in the standard model. • No authority can independently decrypt any ciphertext.

11. 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.

12. Our Results : The number of CAs. : The number of AAs.

13. The rest of this presentation… Bilinear map and access structure Our construction Extensions

14. Background • Bilinear map: • where and are three distinct primes; • and are cyclic groups of order ; • is a map such that • (1) Bilinear: • (2) Non-Degenerate: , such that has order in . (2,2) (2,3) D C B A • LSSS: Any monotone access structure can be realized by a Linear Secret-Share Scheme (LSSS). An LSSS is a labeled matrix , where is a matrix over and labels each row with a share holder. E.g.,

15. Our MA-CP-ABE Scheme: Idea • Start from the single authority CP-ABE of [LOSTW10]: • are chosen randomly, is a generator of . • . • are chosen randomly. • ,. • are chosen randomly. • Constants satisfy .

16. Our MA-CP-ABE Scheme: Idea • . • are chosen randomly. Bind all attribute-related keys of a user together; Prevent collusion attack from different users (Distinct random for each user); Have no relation with attributes • 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.

17. Our MA-CP-ABE Scheme: Idea • One-CA-Multi-AA • . • . • ,.

18. Our MA-CP-ABE Scheme: Idea Multi-CA-Multi-AA • One-CA-Multi-AA • Problem: • In the One-CA-Multi-AA system, the CA holds the value of , so that it can decrypt all ciphertexts. • Introduce multiple CAs: CA1, , CAD . Each CAd chooses independently, and publishes to the public parameters. • In algorithm, . • Implicitly, we have set that . • Only when all CAs collude together, can they decrypt a ciphertext.

19. User

20. Our MA-CP-ABE Scheme: Idea • Naive Multi-CA-Multi-AA • . • || • . • ,.

21. Our MA-CP-ABE Scheme: Idea Our MA-CP-ABE • Naive Multi-CA-Multi-AA • Problem: • When an attacker corrupts a CA, collusion attack can be launched. • E.g., . 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 . However, • Bob obtains from CA2 ; then obtains from AA1 ; • They set , and submit this to AA2 . AA2 is cheated and believes that this “ is legal, because Bob and Tom control CA1 so that they can generate the valid signature. Then AA2 generates by using this , which is actually for . • For the ciphertext, they can reconstruct by using . --- COLLUSION ATTACK WORKS.

22. 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]. registers to ; uses as the public key corresponding to “attribute (k,d)” When visits , regards as the “attributes” of the user User

23. Our MA-CP-ABE Scheme: Idea Our MA-CP-ABE • Naive Multi-CA-Multi-AA • [LOSTW10]. When visits , regards as the “attributes” of the user: takes the place of • [Ours]. • , • . uses to show to that the corresponding is generated honestly.

24. 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.

25. 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, 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 -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.

26. 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 attribute-based 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.

27. 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.

28. Thanks. Q&A