AttributeBased Cryptography. Lecture 21 And PairingBased Cryptography


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1 AttributeBased Cryptography Lecture 21 And PairingBased Cryptography 1
2 IdentityBased Encryption 2
3 IdentityBased Encryption In PKE, KeyGen produces a random (PK,SK) pair 2
4 IdentityBased Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy publickey (e.g., my name)? 2
5 IdentityBased Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy publickey (e.g., my name)? But no one should be able to pick a PK and find an SK for it 2
6 IdentityBased Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy publickey (e.g., my name)? But no one should be able to pick a PK and find an SK for it But suppose a trusted authority for key generation 2
7 IdentityBased Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy publickey (e.g., my name)? But no one should be able to pick a PK and find an SK for it But suppose a trusted authority for key generation Then: Can it generate a valid (PK,SK) pair for any PK? 2
8 IdentityBased Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy publickey (e.g., my name)? But no one should be able to pick a PK and find an SK for it But suppose a trusted authority for key generation Then: Can it generate a valid (PK,SK) pair for any PK? IdentityBased Encryption: a keyserver (with a master secretkey) that can generate such pairs 2
9 IdentityBased Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy publickey (e.g., my name)? But no one should be able to pick a PK and find an SK for it But suppose a trusted authority for key generation Then: Can it generate a valid (PK,SK) pair for any PK? IdentityBased Encryption: a keyserver (with a master secretkey) that can generate such pairs Encryption will use the master publickey, and the receiver s identity (i.e., fancy publickey) 2
10 IdentityBased Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy publickey (e.g., my name)? But no one should be able to pick a PK and find an SK for it But suppose a trusted authority for key generation Then: Can it generate a valid (PK,SK) pair for any PK? IdentityBased Encryption: a keyserver (with a master secretkey) that can generate such pairs Encryption will use the master publickey, and the receiver s identity (i.e., fancy publickey) In PKE, sender has to retrieve PK for every party it wants to talk to (from a trusted public directory) 2
11 IdentityBased Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy publickey (e.g., my name)? But no one should be able to pick a PK and find an SK for it But suppose a trusted authority for key generation Then: Can it generate a valid (PK,SK) pair for any PK? IdentityBased Encryption: a keyserver (with a master secretkey) that can generate such pairs Encryption will use the master publickey, and the receiver s identity (i.e., fancy publickey) In PKE, sender has to retrieve PK for every party it wants to talk to (from a trusted public directory) In IBE, receiver has to obtain its SK from the authority 2
12 IdentityBased Encryption 3
13 IdentityBased Encryption Security requirement for IBE (will skip formal statement): 3
14 IdentityBased Encryption Security requirement for IBE (will skip formal statement): Environment/adversary decides the ID of the honest parties (in the beginning or later on) 3
15 IdentityBased Encryption Security requirement for IBE (will skip formal statement): Environment/adversary decides the ID of the honest parties (in the beginning or later on) Adversary can adaptively request SK for any number of IDs (which are not used for honest parties) 3
16 IdentityBased Encryption Security requirement for IBE (will skip formal statement): Environment/adversary decides the ID of the honest parties (in the beginning or later on) Adversary can adaptively request SK for any number of IDs (which are not used for honest parties) Semantic security for encryption with the ID of honest parties (CPA: with no access to decryption) 3
17 IdentityBased Encryption Security requirement for IBE (will skip formal statement): Environment/adversary decides the ID of the honest parties (in the beginning or later on) Adversary can adaptively request SK for any number of IDs (which are not used for honest parties) Semantic security for encryption with the ID of honest parties (CPA: with no access to decryption) Or, CCA security: also gets (guarded) access to decryption for honest parties IDs 3
18 IdentityBased Encryption Security requirement for IBE (will skip formal statement): Environment/adversary decides the ID of the honest parties (in the beginning or later on) Adversary can adaptively request SK for any number of IDs (which are not used for honest parties) Semantic security for encryption with the ID of honest parties (CPA: with no access to decryption) Or, CCA security: also gets (guarded) access to decryption for honest parties IDs IBE (even CPAsecure) can easily give CCAsecure PKE! 3
19 IdentityBased Encryption Security requirement for IBE (will skip formal statement): Environment/adversary decides the ID of the honest parties (in the beginning or later on) Adversary can adaptively request SK for any number of IDs (which are not used for honest parties) Semantic security for encryption with the ID of honest parties (CPA: with no access to decryption) Or, CCA security: also gets (guarded) access to decryption for honest parties IDs IBE (even CPAsecure) can easily give CCAsecure PKE! IBE: Can t malleate ciphertext for one ID into one for another 3
20 IdentityBased Encryption Security requirement for IBE (will skip formal statement): Environment/adversary decides the ID of the honest parties (in the beginning or later on) Adversary can adaptively request SK for any number of IDs (which are not used for honest parties) Semantic security for encryption with the ID of honest parties (CPA: with no access to decryption) Or, CCA security: also gets (guarded) access to decryption for honest parties IDs IBE (even CPAsecure) can easily give CCAsecure PKE! IBE: Can t malleate ciphertext for one ID into one for another PKEnc MPK (m) = (verkey, C=IBEnc MPK (id=verkey; m), sign signkey (C) ) 3
21 IdentityBased Encryption Security requirement for IBE (will skip formal statement): Environment/adversary decides the ID of the honest parties (in the beginning or later on) Adversary can adaptively request SK for any number of IDs (which are not used for honest parties) Semantic security for encryption with the ID of honest parties (CPA: with no access to decryption) Or, CCA security: also gets (guarded) access to decryption for honest parties IDs IBE (even CPAsecure) can easily give CCAsecure PKE! IBE: Can t malleate ciphertext for one ID into one for another PKEnc MPK (m) = (verkey, C=IBEnc MPK (id=verkey; m), sign signkey (C) ) Digital Signature 3
22 IdentityBased Encryption 4
23 IdentityBased Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) 4
24 IdentityBased Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identitybased noninteractive keydistribution scheme by SakaiOhgishiKasahara (2000) using bilinearpairings and a random oracle 4
25 IdentityBased Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identitybased noninteractive keydistribution scheme by SakaiOhgishiKasahara (2000) using bilinearpairings and a random oracle But no formal proof of security 4
26 IdentityBased Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identitybased noninteractive keydistribution scheme by SakaiOhgishiKasahara (2000) using bilinearpairings and a random oracle But no formal proof of security Quadratic Residuosity based scheme by Cocks (2001) 4
27 IdentityBased Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identitybased noninteractive keydistribution scheme by SakaiOhgishiKasahara (2000) using bilinearpairings and a random oracle But no formal proof of security Quadratic Residuosity based scheme by Cocks (2001) But long ciphertexts (Shorter, but slower scheme by BonehGentryHamburg (2007) ) 4
28 IdentityBased Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identitybased noninteractive keydistribution scheme by SakaiOhgishiKasahara (2000) using bilinearpairings and a random oracle But no formal proof of security Quadratic Residuosity based scheme by Cocks (2001) But long ciphertexts (Shorter, but slower scheme by BonehGentryHamburg (2007) ) BonehFranklin IBE (2001): similar to SKO IDNIKD (but with a proof of security in the random oracle model) 4
29 IdentityBased Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identitybased noninteractive keydistribution scheme by SakaiOhgishiKasahara (2000) using bilinearpairings and a random oracle But no formal proof of security Quadratic Residuosity based scheme by Cocks (2001) But long ciphertexts (Shorter, but slower scheme by BonehGentryHamburg (2007) ) BonehFranklin IBE (2001): similar to SKO IDNIKD (but with a proof of security in the random oracle model) Pairingbased, without RO: BonehBoyen (2004), Waters (2005),... 4
30 IdentityBased Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identitybased noninteractive keydistribution scheme by SakaiOhgishiKasahara (2000) using bilinearpairings and a random oracle But no formal proof of security Quadratic Residuosity based scheme by Cocks (2001) But long ciphertexts (Shorter, but slower scheme by BonehGentryHamburg (2007) ) BonehFranklin IBE (2001): similar to SKO IDNIKD (but with a proof of security in the random oracle model) Pairingbased, without RO: BonehBoyen (2004), Waters (2005),... Without pairing: Using QR, Lattices,... 4
31 Bilinear Pairing 5
32 Bilinear Pairing A relatively new (and less understood) tool 5
33 Bilinear Pairing A relatively new (and less understood) tool Two (or three) groups with an efficient pairing operation, e: G x G G T that is bilinear 5
34 Bilinear Pairing A relatively new (and less understood) tool Two (or three) groups with an efficient pairing operation, e: G x G G T that is bilinear Typically, prime order (cyclic) groups 5
35 Bilinear Pairing A relatively new (and less understood) tool Two (or three) groups with an efficient pairing operation, e: G x G G T that is bilinear Typically, prime order (cyclic) groups e(g a,h b ) = e(g,h) ab 5
36 Bilinear Pairing A relatively new (and less understood) tool Two (or three) groups with an efficient pairing operation, e: G x G G T that is bilinear Typically, prime order (cyclic) groups e(g a,h b ) = e(g,h) ab Multiplication (once) in the exponent! 5
37 Bilinear Pairing A relatively new (and less understood) tool Two (or three) groups with an efficient pairing operation, e: G x G G T that is bilinear Typically, prime order (cyclic) groups e(g a,h b ) = e(g,h) ab Multiplication (once) in the exponent! e(g a g a,g b ) = e(g a,g b ) e(g a,g b ) ; e(g a,g bc ) = e(g ac,g b ) ;... 5
38 Bilinear Pairing A relatively new (and less understood) tool Two (or three) groups with an efficient pairing operation, e: G x G G T that is bilinear Typically, prime order (cyclic) groups e(g a,h b ) = e(g,h) ab Multiplication (once) in the exponent! e(g a g a,g b ) = e(g a,g b ) e(g a,g b ) ; e(g a,g bc ) = e(g ac,g b ) ;... Not degenerate: e(g,g,)! 1 5
39 Decisional Bilinear DiffieHellman Assumption 6
40 Decisional Bilinear DiffieHellman Assumption DDH is not hard in G, if there is a bilinear pairing 6
41 Decisional Bilinear DiffieHellman Assumption DDH is not hard in G, if there is a bilinear pairing Given (g a,g b,g z ) check if e(g a,g b ) = e(g z,g) 6
42 Decisional Bilinear DiffieHellman Assumption DDH is not hard in G, if there is a bilinear pairing Given (g a,g b,g z ) check if e(g a,g b ) = e(g z,g) Decisional Bilinear DH assumption: (g a,g b,g c,g abc ) is indistinguishable from (g a,g b,g c,g z ). (a,b,c,z random) 6
43 IBE from Pairing 7
44 IBE from Pairing MPK: g,h, Y=e(g,h) y, " = (u,u 1,...,u n ) 7
45 IBE from Pairing MPK: g,h, Y=e(g,h) y, " = (u,u 1,...,u n ) MSK: h y 7
46 IBE from Pairing MPK: g,h, Y=e(g,h) y, " = (u,u 1,...,u n ) MSK: h y Enc(m;s) = ( g s, "(ID) s, M.Y s ) 7
47 IBE from Pairing MPK: g,h, Y=e(g,h) y, " = (u,u 1,...,u n ) MSK: h y "(ID) = u Π u i i:id i =1 Enc(m;s) = ( g s, "(ID) s, M.Y s ) 7
48 IBE from Pairing MPK: g,h, Y=e(g,h) y, " = (u,u 1,...,u n ) MSK: h y "(ID) = u Π u i i:id i =1 Enc(m;s) = ( g s, "(ID) s, M.Y s ) SK for ID: ( h y."(id) t, g t ) = (d 1, d 2 ) 7
49 IBE from Pairing MPK: g,h, Y=e(g,h) y, " = (u,u 1,...,u n ) MSK: h y "(ID) = u Π u i i:id i =1 Enc(m;s) = ( g s, "(ID) s, M.Y s ) SK for ID: ( h y."(id) t, g t ) = (d 1, d 2 ) Dec ( a, b, c; d 1, d 2 ) = c/ [ e(b,d 2 ) / e(a,d 1 ) ] 7
50 IBE from Pairing MPK: g,h, Y=e(g,h) y, " = (u,u 1,...,u n ) MSK: h y "(ID) = u Π u i i:id i =1 Enc(m;s) = ( g s, "(ID) s, M.Y s ) SK for ID: ( h y."(id) t, g t ) = (d 1, d 2 ) Dec ( a, b, c; d 1, d 2 ) = c/ [ e(b,d 2 ) / e(a,d 1 ) ] CPA security based on DecisionalBDH 7
51 AttributeBased Encryption 8
52 AttributeBased Encryption Which users can decrypt a ciphertext will be decided by the attributes and policies associated with the message and the user 8
53 AttributeBased Encryption Which users can decrypt a ciphertext will be decided by the attributes and policies associated with the message and the user A central authority will create secret keys for the users (like in IBE) based on attributes/policies for each user 8
54 AttributeBased Encryption Which users can decrypt a ciphertext will be decided by the attributes and policies associated with the message and the user A central authority will create secret keys for the users (like in IBE) based on attributes/policies for each user Ciphertexts can be created (by anyone) by incorporating attributes/policies 8
55 CiphertextPolicy ABE 9
56 CiphertextPolicy ABE Users in the system have attributes; receives a key (or key bundle ) from an authority for its set of attributes 9
57 CiphertextPolicy ABE Users in the system have attributes; receives a key (or key bundle ) from an authority for its set of attributes Ciphertext contains a policy (a boolean predicate over the attribute space) 9
58 CiphertextPolicy ABE Users in the system have attributes; receives a key (or key bundle ) from an authority for its set of attributes Ciphertext contains a policy (a boolean predicate over the attribute space) If a user s attribute set satisfies the policy, can use its key bundle to decrypt the ciphertext 9
59 CiphertextPolicy ABE Users in the system have attributes; receives a key (or key bundle ) from an authority for its set of attributes Ciphertext contains a policy (a boolean predicate over the attribute space) If a user s attribute set satisfies the policy, can use its key bundle to decrypt the ciphertext Multiple users cannot pool their attributes together 9
60 CiphertextPolicy ABE Users in the system have attributes; receives a key (or key bundle ) from an authority for its set of attributes Ciphertext contains a policy (a boolean predicate over the attribute space) If a user s attribute set satisfies the policy, can use its key bundle to decrypt the ciphertext Multiple users cannot pool their attributes together Application: EndtoEnd privacy in AttributeBased Messaging 9
61 KeyPolicy ABE 10
62 KeyPolicy ABE Attributes will be assigned to a ciphertext (when creating the ciphertext) 10
63 KeyPolicy ABE Attributes will be assigned to a ciphertext (when creating the ciphertext) Policies will be assigned to users/keys by an authority (who creates the keys) 10
64 KeyPolicy ABE Attributes will be assigned to a ciphertext (when creating the ciphertext) Policies will be assigned to users/keys by an authority (who creates the keys) A key can decrypt only those ciphertexts whose attributes satisfy the policy 10
65 KeyPolicy ABE Attributes will be assigned to a ciphertext (when creating the ciphertext) Policies will be assigned to users/keys by an authority (who creates the keys) A key can decrypt only those ciphertexts whose attributes satisfy the policy E.g. Applications 10
66 KeyPolicy ABE Attributes will be assigned to a ciphertext (when creating the ciphertext) Policies will be assigned to users/keys by an authority (who creates the keys) A key can decrypt only those ciphertexts whose attributes satisfy the policy E.g. Applications Fuzzy IBE: use a policy that allows receiver s ID to be slightly different from the one in the policy 10
67 KeyPolicy ABE Attributes will be assigned to a ciphertext (when creating the ciphertext) Policies will be assigned to users/keys by an authority (who creates the keys) A key can decrypt only those ciphertexts whose attributes satisfy the policy E.g. Applications Fuzzy IBE: use a policy that allows receiver s ID to be slightly different from the one in the policy Audit log inspection: grant auditor authority to read only messages with certain attributes 10
68 A KPABE Scheme 11
69 A KPABE Scheme A construction that supports linear policies 11
70 A KPABE Scheme A construction that supports linear policies Policy corresponds to a (monotonic) access structure (sets of attributes that when pooled satisfy the policy) 11
71 A KPABE Scheme A construction that supports linear policies Policy corresponds to a (monotonic) access structure (sets of attributes that when pooled satisfy the policy) Linear: Matrix L with each row labeled by an attribute, such that 11
72 A KPABE Scheme A construction that supports linear policies Policy corresponds to a (monotonic) access structure (sets of attributes that when pooled satisfy the policy) Linear: Matrix L with each row labeled by an attribute, such that a set of attributes S satisfies the policy iff there is a vector v such that v.l=[ ] 11
73 A KPABE Scheme A construction that supports linear policies Policy corresponds to a (monotonic) access structure (sets of attributes that when pooled satisfy the policy) Linear: Matrix L with each row labeled by an attribute, such that a set of attributes S satisfies the policy iff there is a vector v such that v.l=[ ] and, labels corresponding to nonzero entries of v are all contained in S 11
74 A KPABE Scheme A construction that supports linear policies Policy corresponds to a (monotonic) access structure (sets of attributes that when pooled satisfy the policy) Linear: Matrix L with each row labeled by an attribute, such that a set of attributes S satisfies the policy iff there is a vector v such that v.l=[ ] and, labels corresponding to nonzero entries of v are all contained in S Linear algebra over some finite field (e.g. GF(p) ) 11
75 A KPABE Scheme A construction that supports linear policies Policy corresponds to a (monotonic) access structure (sets of attributes that when pooled satisfy the policy) Linear: Matrix L with each row labeled by an attribute, such that a set of attributes S satisfies the policy iff there is a vector v such that v.l=[ ] and, labels corresponding to nonzero entries of v are all contained in S Linear algebra over some finite field (e.g. GF(p) ) For efficiency need a small matrix 11
76 Example of a Linear Policy 12
77 Example of a Linear Policy Consider this policy, over 7 attributes 12
78 Example of a Linear Policy Consider this policy, over 7 attributes OR AND AND AND OR 12
79 Example of a Linear Policy Consider this policy, over 7 attributes OR L: AND AND AND OR 12
80 Example of a Linear Policy Consider this policy, over 7 attributes OR L: AND AND AND OR
81 Example of a Linear Policy Consider this policy, over 7 attributes OR L: AND AND AND OR Can allow threshold gates too 12
82 A KPABE Scheme 13
83 A KPABE Scheme MPK: g, Y=e(g,g) y, T = (g t1,..., g tn ) (n attributes) 13
84 A KPABE Scheme MPK: g, Y=e(g,g) y, T = (g t1,..., g tn ) (n attributes) MSK: t a for each attribute 13
85 A KPABE Scheme MPK: g, Y=e(g,g) y, T = (g t1,..., g tn ) (n attributes) MSK: t a for each attribute Enc(m,A;s) = ( A, { T a s } a A, M.Y s ) 13
86 A KPABE Scheme MPK: g, Y=e(g,g) y, T = (g t1,..., g tn ) (n attributes) MSK: t a for each attribute Enc(m,A;s) = ( A, { T a s } a A, M.Y s ) SK for policy L (with d rows): Let u=(u 1... u d ) s.t. Σ i u i = y. For each row i, let x i = <L i,u>/t label(i). Let Key = { g xi } i=1 to d 13
87 A KPABE Scheme MPK: g, Y=e(g,g) y, T = (g t1,..., g tn ) (n attributes) MSK: t a for each attribute Enc(m,A;s) = ( A, { T a s } a A, M.Y s ) SK for policy L (with d rows): Let u=(u 1... u d ) s.t. Σ i u i = y. For each row i, let x i = <L i,u>/t label(i). Let Key = { g xi } i=1 to d Dec ( (A,{U a } a A,c); {X i } row i ) : Get Y s = Π i:label(i) A e(u label(i),x i ) vi where v = [v 1... v d ] s.t. v i =0 if label(i) A, and vl=[1...1] 13
88 A KPABE Scheme MPK: g, Y=e(g,g) y, T = (g t1,..., g tn ) (n attributes) MSK: t a for each attribute Enc(m,A;s) = ( A, { T a s } a A, M.Y s ) SK for policy L (with d rows): Let u=(u 1... u d ) s.t. Σ i u i = y. For each row i, let x i = <L i,u>/t label(i). Let Key = { g xi } i=1 to d Dec ( (A,{U a } a A,c); {X i } row i ) : Get Y s = Π i:label(i) A e(u label(i),x i ) vi where v = [v 1... v d ] s.t. v i =0 if label(i) A, and vl=[1...1] CPA security based on DecisionalBDH 13
89 A KPABE Scheme MPK: g, Y=e(g,g) y, T = (g t1,..., g tn ) (n attributes) MSK: t a for each attribute Enc(m,A;s) = ( A, { T a s } a A, M.Y s ) SK for policy L (with d rows): Let u=(u 1... u d ) s.t. Σ i u i = y. For each row i, let x i = <L i,u>/t label(i). Let Key = { g xi } i=1 to d Dec ( (A,{U a } a A,c); {X i } row i ) : Get Y s = Π i:label(i) A e(u label(i),x i ) vi where v = [v 1... v d ] s.t. v i =0 if label(i) A, and vl=[1...1] CPA security based on DecisionalBDH Choosing a random vector u for each key helps in preventing collusion 13
90 Predicate Encryption 14
91 Predicate Encryption Similar to ABE, but the ciphertext hides the attributes/ policy 14
92 Predicate Encryption Similar to ABE, but the ciphertext hides the attributes/ policy Decryption reveals only whether a condition is satisfied by the ciphertext, and if it is, reveals the message too 14
93 Predicate Encryption Similar to ABE, but the ciphertext hides the attributes/ policy Decryption reveals only whether a condition is satisfied by the ciphertext, and if it is, reveals the message too e.g.: ciphertext contains a vector c, and key a vector d. Predicate: whether <c,d> = 0 or not 14
94 Predicate Encryption Similar to ABE, but the ciphertext hides the attributes/ policy Decryption reveals only whether a condition is satisfied by the ciphertext, and if it is, reveals the message too e.g.: ciphertext contains a vector c, and key a vector d. Predicate: whether <c,d> = 0 or not A building block for other predicates 14
95 Predicate Encryption Similar to ABE, but the ciphertext hides the attributes/ policy Decryption reveals only whether a condition is satisfied by the ciphertext, and if it is, reveals the message too e.g.: ciphertext contains a vector c, and key a vector d. Predicate: whether <c,d> = 0 or not A building block for other predicates Constructions using stronger ( nonstandard ) assumptions 14
96 AttributeBased Signatures 15
97 AttributeBased Signatures Claimandendorse : Claim to have attributes satisfying a certain policy, and sign a message 15
98 AttributeBased Signatures Claimandendorse : Claim to have attributes satisfying a certain policy, and sign a message Soundness: can t forge, even by colluding 15
99 AttributeBased Signatures Claimandendorse : Claim to have attributes satisfying a certain policy, and sign a message Soundness: can t forge, even by colluding Hiding: Verification without learning how the policy was satisfied 15
100 AttributeBased Signatures Claimandendorse : Claim to have attributes satisfying a certain policy, and sign a message Soundness: can t forge, even by colluding Hiding: Verification without learning how the policy was satisfied Also unlinkable: cannot link multiple signatures as originating from the same signer 15
101 An ABS Construction 16
102 An ABS Construction Using Credential Bundles and NIZK proofs (in fact, NIWI proofs) 16
103 An ABS Construction Using Credential Bundles and NIZK proofs (in fact, NIWI proofs) Credential Bundle for a set of attributes: 16
104 An ABS Construction Using Credential Bundles and NIZK proofs (in fact, NIWI proofs) Credential Bundle for a set of attributes: Given multiple credential bundles, can t create a credential bundle for a new set, unless it is a subset of attributes in a single given credential bundle 16
105 An ABS Construction Using Credential Bundles and NIZK proofs (in fact, NIWI proofs) Credential Bundle for a set of attributes: Given multiple credential bundles, can t create a credential bundle for a new set, unless it is a subset of attributes in a single given credential bundle Map each (claim,message) to a pseudoattribute 16
106 An ABS Construction Using Credential Bundles and NIZK proofs (in fact, NIWI proofs) Credential Bundle for a set of attributes: Given multiple credential bundles, can t create a credential bundle for a new set, unless it is a subset of attributes in a single given credential bundle Map each (claim,message) to a pseudoattribute Signing key: credential bundle for (real) attributes possessed 16
107 An ABS Construction Using Credential Bundles and NIZK proofs (in fact, NIWI proofs) Credential Bundle for a set of attributes: Given multiple credential bundles, can t create a credential bundle for a new set, unless it is a subset of attributes in a single given credential bundle Map each (claim,message) to a pseudoattribute Signing key: credential bundle for (real) attributes possessed Signature: a NIZK proof of knowledge of a credentialbundle for attributes satisfying the claim, or a credential for the pseudoattribute corresponding to (claim,message) 16
108 An ABS Construction Using Credential Bundles and NIZK proofs (in fact, NIWI proofs) Credential Bundle for a set of attributes: Given multiple credential bundles, can t create a credential bundle for a new set, unless it is a subset of attributes in a single given credential bundle Map each (claim,message) to a pseudoattribute Signing key: credential bundle for (real) attributes possessed Signature: a NIZK proof of knowledge of a credentialbundle for attributes satisfying the claim, or a credential for the pseudoattribute corresponding to (claim,message) Using conventional tools. More efficiently using bilinear pairings. 16
109 Today 17
110 Today IBE, ABE and ABS 17
111 Today IBE, ABE and ABS Pairingbased cryptography 17
112 Today IBE, ABE and ABS Pairingbased cryptography Next up: 17
113 Today IBE, ABE and ABS Pairingbased cryptography Next up: Some more applications of pairingbased cryptography 17
114 Today IBE, ABE and ABS Pairingbased cryptography Next up: Some more applications of pairingbased cryptography Generic groups 17
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