Structure-Preserving Certificateless Encryption and Its Application
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1 SESSION ID: CRYP-T06 Structure-Preserving Certificateless Encryption and Its Application Prof. Sherman S. M. Chow Department of Information Engineering Chinese University of Hong Kong, Hong joint work with Tao Zhang and Huangting Wu CUHK Tencent CUHK
2 Modular Design Reduction in Cost Flexibility in Design 1/28
3 Some Traditional Views To use a modular approach in designing cryptosystem means it would be insecure since mix-and-match types of attack will succeed it would be hopelessly inefficient when compared to a specific design To use public key encryption, we need public-key infrastructure. To issue a signature, everyone knows who is the signer. To ensure anonymity, we would lose accountability. 2/28
4 Modern Cryptography To use a modular approach in designing cryptosystem means Structure-Preserving Cryptography is a framework it would be insecure since mix-and-match types of attack will succeed for securely & efficiently realizing a generic design. it would be hopelessly inefficient when compared to a specific design To use public key encryption, we need public-key infrastructure. Certificateless Encryption does not require any PKI. To issue a signature, everyone knows who is the signer. Group Signature ensures Signer-Anonymity and To ensure anonymity, we would lose accountability. Accountability simultaneously. 3/28
5 Rundown Structure-Preserving Cryptography Certificateless Encryption Structure-Preserving Certificateless Encryption and Its New Application (in Group Signatures with Certified Limited Opening ) 4/28
6 Structure-Preserving Cryptography (and Bilinear Groups and Groth-Sahai Proof System)
7 Structure-Preserving Cryptography A framework for securely and efficiently instantiating a design But why it can be efficient? Because all of the building blocks use the same structure Suppose we compose encryption and signature together. Encryption is based on a group Signature is based on the same group What kind of group is popular? Bilinear group! 6/28
8 Bilinear Groups G, H, and G T are 3 multiplicative cyclic group of prime order p. e: G x H (base groups) G T (target group) is bilinear: g G, h H, x, y Z p, e(g, h) = e(g, h) xy Why is it useful? We can multiply the secret exponents! Discrete logarithm is still hard: given g, g x, cannot recover x. 7/28
9 Structure-Preserving Cryptography for Bilinear Groups All public objects (public-key, messages, signatures, etc.) merely consists of elements in G and H. Verifying relations of interest can be done only by group op. s, membership testing, and evaluating pairing product equations: Π i e(a i, Y i ) Π i e(b i, X i ) Π i Π j e(x i, Y j ) c ij = T where {c ij } and T are system-defined constants. Every building blocks follow the same form. But why it can be secure? Groth Sahai proof system (Eurocrypt 08) can prove about it without leaking {A i }, {B i }, {X i }, {Y i }! 8/28
10 Certificateless Encryption (and why it is better than Identity-Based Encryption)
11 Identity-Based Encryption (IBE) - Public System Parameter - Bob knows Alice Hey guys! I m Alice~ Encrypt to Alice 10/28
12 Who can decrypt? Authenticated Users and KGC Generate ID-based Secret Key (using Master Secret) Alice Alice Alice the Receiver Authenticated Get an ID-based secret key 11/28
13 Certificateless Encryption (CLE) but not I have E71434 CEO Name := Alice Public Key := E FA80C EBED912 E Hey~ CEO! Encryption keys CEO ID-based user secret key E71434 PKE decryption key CEO E /28
14 Benefits of Certificateless Encryption In essence, CLE = PKE + IBE (+strong decryption oracle, cf., Chow Franklin Zhang in CT-RSA 14) Implicit certificate (better than PKE) The encryptor does not need to verify any certificate. Only the right person can get the partial decryption key from the KGC. Free from key-escrow (better than IBE) The KGC does not know the user private key. 13/28
15 Structure-Preserving Certificateless Encryption a new primitive in Structure-Preserving Cryptography
16 Upgrade from Structure-Preserving IBE? There is no known construction of structure-preserving (SP) IBE. Only partial SP-IBE exists (ID is not a group element). proposed by Libert Joye in CT-RSA 14 IBE Signature, i.e., the ID-based secret key is a signature on ID IBE decryption: pairing up this signature with the ciphertext. Can we upgrade structure-preserving signatures (SPS) to IBE? Verification of existing SPS requires computing a pairing where both of the input elements come from the signature. 15/28
17 Upgrade from Structure-Preserving PKE? If not SP-IBE, how about using SP-PKE? How to ensure that the user public key is still related to the master public key of the IBE system? Otherwise, even if you are not the CEO, you can claim to be and decrypt. Ask the encryptor to somehow check the user public key? May work in principle but it is rather meaningless CLE is for relieving the encryptors from verifying a certificate And now you are asking them to verify a public key? 16/28
18 Our Idea: upgrades from Structure-Preserving Signature We employ an SP signature scheme by Abe et al. in Crypto 11. For public key (g, h, W 1, W 2, V 1, V 2 ), verification equations are: e(w 2, R) e(g, S) e(u, M 0 ) = e(w 1, h) e(t, R) e(m 1, V 1 ) e(m 2, V 2 ) = e(g, h) where (R, S, T) is a signature on the message vector (M 0, M 1, M 2 ) Trick 1: we use the signature (R, S, T) to also sign on M 0 = R Trick 2: we set M 1 as the identity and M 2 as a user public key 17/28
19 High-Level Idea of the Conversion Public Key of SPS Master Public Key of SP-CLE Signature of SPS Partial Private Key of the User We exploit the elements in the pairing product equations of SPS. Some elements embedded the encryption randomness. Only valid verification equations can recover the randomness. But how? 18/28
20 More Details of the Conversion e(w 2, R) e(g, S) e(u, R) = e(w 1, h) // R, S, T are now private e(t, R) e(id, V 1 ) e(d, V 2 ) = e(g, h) // where D is a user public key The choice depends on the input elements of a pairing. Both elements are public: we make them the session key. One of the elements is public: we embed the randomness. Both elements are private (which is also why SP-IBE plan fails): we publish one element (R in our case) as a user public key too. 19/28
21 Spelling out the details e(w 2, R) e(g, S) e(u, R) = e(w 1, h) // e(g, S): only S is private e(t, R) e(id, V 1 ) e(d, V 2 ) = e(g, h) // e(t, R): only T is private C 0 = M K, C g = g x, C R = R y, C z = g z // M is the message to encrypt K = {e(w 2, R) e(u, R) / e(w 1, h)} x // K is the session key {e(id, V 1 ) e(d, V 2 ) / e(g, h)} y e(d, h z ) 20/28
22 Making it preserving more structure Message is in the target group G T. Ciphertext has many elements in the target group G T. We can exploit the tricks of Libert Joye to resolve these. 21/28
23 Group Signatures with Certified Limited Opening a new primitive for Accountable Privacy
24 Group Signatures Group-oriented signatures with anonymity but with an explicit group formation (diff. from ring signature) A group manager (GM) issues credentials Any member can sign for the group remain anonymous within the group signatures are unlinkable but, unconditional anonymity may be abused, we want accountability An opening authority (OA) can open a group signature to reveal its true signer 23/28
25 Group Signatures with Message-Dependent Opening OA is too powerful. Message-dependent opening introduces another admitter. The admitter generates a message-dependent opening key. Opening only works with both master opening key and this message-dependent opening key. Good: opening power is restricted Bad: always bother the OA 24/28
26 Group Signatures with Certified Limited Opening (CLO) Opening in message-dependent opening depends on the message... We generalize it to contexts. Instead of the admitter, we introduce a certifier. The certifier certifies the opener depending on the context. i.e., the opening power is limited to only the specified context. No need to bother the OA. The opener s opening power is limited. No (un-certified) opener can open signatures in other contexts. 25/28
27 Applications in Electronic Voting Consider using the group signatures for signing on votes. The government can be the master certifier. The openers can be those special party overseeing different districts/counties/provinces/states different contexts. Open when something bad happen, e.g., when the voting software in one of the voting booths could be compromised. 26/28
28 Structure-Preserving CLE Group Signatures with CLO SP-CLE s identity Context in Group Sig. with CLO Group signature = Verifiable encryption of the signer s identity with respect to the corresponding context. SP-CLE key issuing Certifying the opening power. SP-CLE decryption Opening of identity limited to the context. 27/28
29 Conclusion Structure-Preserving Cryptography for Modular design Certificateless Encryption for Escrow-Free Encryption w/o PKI Structure-Preserving Certificateless Encryption a new tool in structure-preserving cryptography and Its Application (in Group Signatures with Certified Limited Opening ) a new tool for accountable privacy Sherman S. M. Chow <{firstname}[at]ie.cuhk.edu.hk> 28/28
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