# Attribute-Based Cryptography. Lecture 21 And Pairing-Based Cryptography

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Attribute-Based Cryptography Lecture 21 And Pairing-Based Cryptography 1

2 Identity-Based Encryption 2

3 Identity-Based Encryption In PKE, KeyGen produces a random (PK,SK) pair 2

4 Identity-Based Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy public-key (e.g., my name)? 2

5 Identity-Based Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy public-key (e.g., my name)? But no one should be able to pick a PK and find an SK for it 2

6 Identity-Based Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy public-key (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 Identity-Based Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy public-key (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 Identity-Based Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy public-key (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? Identity-Based Encryption: a key-server (with a master secret-key) that can generate such pairs 2

9 Identity-Based Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy public-key (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? Identity-Based Encryption: a key-server (with a master secret-key) that can generate such pairs Encryption will use the master public-key, and the receiver s identity (i.e., fancy public-key) 2

10 Identity-Based Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy public-key (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? Identity-Based Encryption: a key-server (with a master secret-key) that can generate such pairs Encryption will use the master public-key, and the receiver s identity (i.e., fancy public-key) In PKE, sender has to retrieve PK for every party it wants to talk to (from a trusted public directory) 2

11 Identity-Based Encryption In PKE, KeyGen produces a random (PK,SK) pair Can I have a fancy public-key (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? Identity-Based Encryption: a key-server (with a master secret-key) that can generate such pairs Encryption will use the master public-key, and the receiver s identity (i.e., fancy public-key) 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 Identity-Based Encryption 3

13 Identity-Based Encryption Security requirement for IBE (will skip formal statement): 3

14 Identity-Based 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 Identity-Based 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 Identity-Based 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 Identity-Based 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 Identity-Based 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 CPA-secure) can easily give CCA-secure PKE! 3

19 Identity-Based 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 CPA-secure) can easily give CCA-secure PKE! IBE: Can t malleate ciphertext for one ID into one for another 3

20 Identity-Based 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 CPA-secure) can easily give CCA-secure 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 Identity-Based 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 CPA-secure) can easily give CCA-secure 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 Identity-Based Encryption 4

23 Identity-Based Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) 4

24 Identity-Based Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identity-based non-interactive key-distribution scheme by Sakai-Ohgishi-Kasahara (2000) using bilinear-pairings and a random oracle 4

25 Identity-Based Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identity-based non-interactive key-distribution scheme by Sakai-Ohgishi-Kasahara (2000) using bilinear-pairings and a random oracle But no formal proof of security 4

26 Identity-Based Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identity-based non-interactive key-distribution scheme by Sakai-Ohgishi-Kasahara (2000) using bilinear-pairings and a random oracle But no formal proof of security Quadratic Residuosity based scheme by Cocks (2001) 4

27 Identity-Based Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identity-based non-interactive key-distribution scheme by Sakai-Ohgishi-Kasahara (2000) using bilinear-pairings 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 Boneh-Gentry-Hamburg (2007) ) 4

28 Identity-Based Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identity-based non-interactive key-distribution scheme by Sakai-Ohgishi-Kasahara (2000) using bilinear-pairings 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 Boneh-Gentry-Hamburg (2007) ) Boneh-Franklin IBE (2001): similar to SKO ID-NIKD (but with a proof of security in the random oracle model) 4

29 Identity-Based Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identity-based non-interactive key-distribution scheme by Sakai-Ohgishi-Kasahara (2000) using bilinear-pairings 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 Boneh-Gentry-Hamburg (2007) ) Boneh-Franklin IBE (2001): similar to SKO ID-NIKD (but with a proof of security in the random oracle model) Pairing-based, without RO: Boneh-Boyen (2004), Waters (2005),... 4

30 Identity-Based Encryption Notion of IBE suggested by Shamir in 1984 (but no construction) An identity-based non-interactive key-distribution scheme by Sakai-Ohgishi-Kasahara (2000) using bilinear-pairings 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 Boneh-Gentry-Hamburg (2007) ) Boneh-Franklin IBE (2001): similar to SKO ID-NIKD (but with a proof of security in the random oracle model) Pairing-based, without RO: Boneh-Boyen (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- Diffie-Hellman Assumption 6

40 Decisional Bilinear- Diffie-Hellman Assumption DDH is not hard in G, if there is a bilinear pairing 6

41 Decisional Bilinear- Diffie-Hellman 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- Diffie-Hellman 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 Decisional-BDH 7

51 Attribute-Based Encryption 8

52 Attribute-Based Encryption Which users can decrypt a ciphertext will be decided by the attributes and policies associated with the message and the user 8

53 Attribute-Based 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 Attribute-Based 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 Ciphertext-Policy ABE 9

56 Ciphertext-Policy ABE Users in the system have attributes; receives a key (or key bundle ) from an authority for its set of attributes 9

57 Ciphertext-Policy 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 Ciphertext-Policy 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 Ciphertext-Policy 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 Ciphertext-Policy 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: End-to-End privacy in Attribute-Based Messaging 9

61 Key-Policy ABE 10

62 Key-Policy ABE Attributes will be assigned to a ciphertext (when creating the ciphertext) 10

63 Key-Policy 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 Key-Policy 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 Key-Policy 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 Key-Policy 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 Key-Policy 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 KP-ABE Scheme 11

69 A KP-ABE Scheme A construction that supports linear policies 11

70 A KP-ABE 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 KP-ABE 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 KP-ABE 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 KP-ABE 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 non-zero entries of v are all contained in S 11

74 A KP-ABE 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 non-zero entries of v are all contained in S Linear algebra over some finite field (e.g. GF(p) ) 11

75 A KP-ABE 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 non-zero 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 KP-ABE Scheme 13

83 A KP-ABE Scheme MPK: g, Y=e(g,g) y, T = (g t1,..., g tn ) (n attributes) 13

84 A KP-ABE Scheme MPK: g, Y=e(g,g) y, T = (g t1,..., g tn ) (n attributes) MSK: t a for each attribute 13

85 A KP-ABE 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 KP-ABE 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 KP-ABE 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 KP-ABE 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 Decisional-BDH 13

89 A KP-ABE 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 Decisional-BDH 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 ( non-standard ) assumptions 14

96 Attribute-Based Signatures 15

97 Attribute-Based Signatures Claim-and-endorse : Claim to have attributes satisfying a certain policy, and sign a message 15

98 Attribute-Based Signatures Claim-and-endorse : Claim to have attributes satisfying a certain policy, and sign a message Soundness: can t forge, even by colluding 15

99 Attribute-Based Signatures Claim-and-endorse : 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 Attribute-Based Signatures Claim-and-endorse : 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 pseudo-attribute 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 pseudo-attribute 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 pseudo-attribute Signing key: credential bundle for (real) attributes possessed Signature: a NIZK proof of knowledge of a credential-bundle 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 pseudo-attribute Signing key: credential bundle for (real) attributes possessed Signature: a NIZK proof of knowledge of a credential-bundle 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 Pairing-based cryptography 17

112 Today IBE, ABE and ABS Pairing-based cryptography Next up: 17

113 Today IBE, ABE and ABS Pairing-based cryptography Next up: Some more applications of pairing-based cryptography 17

114 Today IBE, ABE and ABS Pairing-based cryptography Next up: Some more applications of pairing-based cryptography Generic groups 17

### Functional Encryption. Lecture 27

Functional Encryption Lecture 27 Functional Encryption Plain encryption: for secure communication. Does not allow modifying encrypted data. Homomorphic Encryption: allows computation on encrypted data,

### Fuzzy Identity-Based Encryption

Fuzzy Identity-Based Encryption Janek Jochheim June 20th 2013 Overview Overview Motivation (Fuzzy) Identity-Based Encryption Formal definition Security Idea Ingredients Construction Security Extensions

### Identity-Based Encryption. Gregory Neven (IBM Zurich Research Laboratory) Eike Kiltz (CWI Amsterdam)

Identity-Based Encryption Gregory Neven (IBM Zurich Research Laboratory) Eike Kiltz (CWI Amsterdam) Public-key encryption PKI pk KeyGen sk M Enc C Dec M Sender (pk) Receiver (sk) 2 Identity-based encryption

### Identity-Based Encryption: A 30-Minute Tour. Palash Sarkar

Identity-Based Encryption: A 30-Minute Tour Palash Sarkar Applied Statistics Unit Indian Statistical Institute, Kolkata India palash@isical.ac.in Palash Sarkar (ISI, Kolkata) IBE: Some Issues ISI, Kolkata,

### Categorical Heuristic for Attribute Based Encryption in the Cloud Server

Categorical Heuristic for Attribute Based Encryption in the Cloud Server R. Brindha 1, R. Rajagopal 2 1( M.E, Dept of CSE, Vivekanandha Institutes of Engineering and Technology for Women, Tiruchengode,

### Verifiable Outsourced Computations Outsourcing Computations to Untrusted Servers

Outsourcing Computations to Untrusted Servers Security of Symmetric Ciphers in Network Protocols ICMS, May 26, 2015, Edinburgh Problem Motivation Problem Motivation Problem Motivation Problem Motivation

### Cryptography. Identity-based Encryption. Jean-Sébastien Coron and David Galindo. May 15, 2014. Université du Luxembourg

Identity-based Encryption Université du Luxembourg May 15, 2014 Summary Identity-Based Encryption (IBE) What is Identity-Based Encryption? Difference with conventional PK cryptography. Applications of

### Outsourcing the Decryption of ABE Ciphertexts

Outsourcing the Decryption of ABE Ciphertexts Matthew Green and Susan Hohenberger Johns Hopkins University Brent Waters UT Austin Background A problem Securing records in a data-sharing environment E.g.,

### Lecture 17: Re-encryption

600.641 Special Topics in Theoretical Cryptography April 2, 2007 Instructor: Susan Hohenberger Lecture 17: Re-encryption Scribe: Zachary Scott Today s lecture was given by Matt Green. 1 Motivation Proxy

### Identity Based Encryption: An Overview

Identity Based Encryption: An Overview Palash Sarkar Indian Statistical Institute IBE Overview p. Structure of Presentation Conceptual overview and motivation. Some technical details. Brief algebraic background.

### Lecture 25: Pairing-Based Cryptography

6.897 Special Topics in Cryptography Instructors: Ran Canetti and Ron Rivest May 5, 2004 Lecture 25: Pairing-Based Cryptography Scribe: Ben Adida 1 Introduction The field of Pairing-Based Cryptography

### Lightweight Encryption for Email

Lightweight Encryption for Email Ben Adida ben@mit.edu 7 July 2005 joint work with Susan Hohenberger and Ronald L. Rivest MIT Cryptography and Information Security Group Motivation To Improve/Restore the

### Efficient File Sharing in Electronic Health Records

Efficient File Sharing in Electronic Health Records Clémentine Gritti, Willy Susilo and Thomas Plantard University of Wollongong, Australia 27/02/2015 1/20 Outline for Section 1 1 Introduction 2 Solution

### Chosen-Ciphertext Security from Identity-Based Encryption

Chosen-Ciphertext Security from Identity-Based Encryption Dan Boneh Ran Canetti Shai Halevi Jonathan Katz Abstract We propose simple and efficient CCA-secure public-key encryption schemes (i.e., schemes

### Key Privacy for Identity Based Encryption

Key Privacy for Identity Based Encryption Internet Security Research Lab Technical Report 2006-2 Jason E. Holt Internet Security Research Lab Brigham Young University c 2006 Brigham Young University March

### Chosen-Ciphertext Security from Identity-Based Encryption

Chosen-Ciphertext Security from Identity-Based Encryption Dan Boneh Ran Canetti Shai Halevi Jonathan Katz June 13, 2006 Abstract We propose simple and efficient CCA-secure public-key encryption schemes

### Breaking An Identity-Based Encryption Scheme based on DHIES

Breaking An Identity-Based Encryption Scheme based on DHIES Martin R. Albrecht 1 Kenneth G. Paterson 2 1 SALSA Project - INRIA, UPMC, Univ Paris 06 2 Information Security Group, Royal Holloway, University

### Public-Key Cryptography. Oregon State University

Public-Key Cryptography Çetin Kaya Koç Oregon State University 1 Sender M Receiver Adversary Objective: Secure communication over an insecure channel 2 Solution: Secret-key cryptography Exchange the key

### CIS 5371 Cryptography. 8. Encryption --

CIS 5371 Cryptography p y 8. Encryption -- Asymmetric Techniques Textbook encryption algorithms In this chapter, security (confidentiality) is considered in the following sense: All-or-nothing secrecy.

### Lecture 2 August 29, 13:40 15:40

Lecture 2 August 29, 13:40 15:40 Public-key encryption with keyword search Anonymous identity-based encryption Identity-based encryption with wildcards Public-key encryption with keyword search & anonymous

### MESSAGE AUTHENTICATION IN AN IDENTITY-BASED ENCRYPTION SCHEME: 1-KEY-ENCRYPT-THEN-MAC

MESSAGE AUTHENTICATION IN AN IDENTITY-BASED ENCRYPTION SCHEME: 1-KEY-ENCRYPT-THEN-MAC by Brittanney Jaclyn Amento A Thesis Submitted to the Faculty of The Charles E. Schmidt College of Science in Partial

### Anonymity and Time in Public-Key Encryption

Anonymity and Time in Public-Key Encryption Elizabeth Anne Quaglia Thesis submitted to the University of London for the degree of Doctor of Philosophy Information Security Group Department of Mathematics

### Outsourcing the Decryption of ABE Ciphertexts

Outsourcing the Decryption of ABE Ciphertexts Matthew Green Johns Hopkins University Susan Hohenberger Johns Hopkins University Brent Waters University of Texas at Austin Abstract Attribute-based encryption

### Secure and Verifiable Policy Update Outsourcing for Big Data Access Control in the Cloud

1 Secure and Verifiable Policy Update Outsourcing for Big Data Access Control in the Cloud Kan Yang Associate Member IEEE Xiaohua Jia Fellow IEEE Kui Ren Senior Member IEEE Abstract Due to the high volume

### Identity Based Encryption

Bar Ilan Winter School. Feb. 2013 Bilinear Pairings in Cryptography: Identity Based Encryption Dan Boneh Stanford University (2 hours) Recall: Pub-Key Encryption (PKE) PKE Three algorithms : (G, E, D)

### Identity-based Encryption with Post-Challenge Auxiliary Inputs for Secure Cloud Applications and Sensor Networks

Identity-based Encryption with Post-Challenge Auxiliary Inputs for Secure Cloud Applications and Sensor Networks Tsz Hon Yuen - Huawei, Singapore Ye Zhang - Pennsylvania State University, USA Siu Ming

### Keywords: Authentication, Third party audit, cloud storage, cloud service provider, Access control.

Volume 5, Issue 3, March 2015 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com Identity Based

### Identity Based Encryption: An Overview

IBE Overview p. 1/6 Identity Based Encryption: An Overview Palash Sarkar Indian Statistical Institute IBE Overview p. 2/6 Structure of Presentation Conceptual overview and motivation. Some technical details.

### Public-Key Encryption (Asymmetric Encryption)

Public-Key Encryption (Asymmetric Encryption) Summer School, Romania 2014 Marc Fischlin 13. Oktober 2010 Dr.Marc Fischlin Kryptosicherheit 1 The story so far (Private-Key Crypto) Alice establish secure

### ID-based Cryptography and Smart-Cards

ID-based Cryptography and Smart-Cards Survol des techniques cryptographiques basées sur l identité et implémentation sur carte à puce The Need for Cryptography Encryption! Transform a message so that only

### Privacy in Encrypted Content Distribution Using Private Broadcast Encryption

Privacy in Encrypted Content Distribution Using Private Broadcast Encryption Adam Barth 1, Dan Boneh 1, and Brent Waters 2 1 Stanford University, Stanford, CA 94305 {abarth, dabo}@cs.stanford.edu 2 SRI

### Secure Group Oriented Data Access Model with Keyword Search Property in Cloud Computing Environment

Secure Group Oriented Data Access Model with Keyword Search Property in Cloud Computing Environment Chih Hung Wang Computer Science and Information Engineering National Chiayi University Chiayi City 60004,

### Wildcarded Identity-Based Encryption

Wildcarded Identity-Based Encryption Michel Abdalla 1, James Birkett 2, Dario Catalano 3, Alexander W. Dent 4, John Malone-Lee 5, Gregory Neven 6,7, Jacob C. N. Schuldt 8, and Nigel P. Smart 9 1 Ecole

### IEEE Draft P1363.3. Identity Based Public Key Cryptography Based On Pairings. Daniel Schliebner. 14. Dezember 2009

Identity Based Public Key Cryptography Based On Pairings 14. Dezember 2009 Gliederung Introduction Identity Based Encryption The Protocol Security Of The Protocol Discussion About The Headline Identity

### Acknowledgements. Notations and abbreviations

Abstract This work explains the fundamental definitions required to define and create Fuzzy Identity- Based Encryption schemes as an error-tolerant version of Identity-Based Encryption schemes, along with

### Data Sharing on Untrusted Storage with Attribute-Based Encryption

Data Sharing on Untrusted Storage with Attribute-Based Encryption by Shucheng Yu A Dissertation Submitted to the Faculty of the WORCESTER POLYTECHNIC INSTITUTE In partial fulfillment of the requirements

### An Introduction to Identity-based Cryptography CSEP 590TU March 2005 Carl Youngblood

An Introduction to Identity-based Cryptography CSEP 590TU March 2005 Carl Youngblood One significant impediment to the widespread adoption of public-key cryptography is its dependence on a public-key infrastructure

### Identity-based encryption and Generic group model (work in progress) Peeter Laud Arvutiteaduse teooriaseminar Tallinn, 05.01.2012

Identity-based encryption and Generic group model (work in progress) Peeter Laud Arvutiteaduse teooriaseminar Tallinn, 05.01.2012 Identity-based encryption Public-key encryption, where public key = name

### Secure and Efficient Data Retrieval Process based on Hilbert Space Filling Curve

Secure and Efficient Data Retrieval Process based on Hilbert Space Filling Curve N.S. Jeya karthikka PG Scholar Sri Ramakrishna Engg Collg S.Bhaggiaraj Assistant Professor Sri Ramakrishna Engg Collg V.Sumathy

### Identity-Based Encryption

Identity-Based ryption Gregory Neven IBM Zurich Research Laboratory gone WILD Public-key encryption PKI pk KeyGen sk M Dec M Sender (pk) Receiver (sk) 2 1 Identity-based encryption (IBE) [S84] Goal: Allow

### Secure Attribute Based Mechanism through Access cipher policy in Outsourced Cloud Data

Secure Attribute Based Mechanism through Access cipher policy in Outsourced Cloud Data V.Abinaya PG Scholar Kalasalingam Institute of Technology Krishnankoil. V.Ramesh Assistant professor Kalasalingam

### Public Key Cryptography. Basic Public Key Cryptography

Public Key Cryptography EJ Jung Basic Public Key Cryptography public key public key? private key Alice Bob Given: Everybody knows Bob s public key - How is this achieved in practice? Only Bob knows the

### Attribute-Based Encryption for Fine-Grained Access Control of Encrypted Data

Attribute-Based Encryption for Fine-Grained Access Control of Encrypted Data Vipul Goyal Omkant Pandey Amit Sahai Brent Waters Abstract As more sensitive data is shared and stored by third-party sites

### Security Strength of RSA and Attribute Based Encryption for Data Security in Cloud Computing

Security Strength of RSA and Attribute Based Encryption for Data Security in Cloud Computing S.Hemalatha, Dr.R.Manickachezian Ph.D Research Scholar, Department of Computer Science, N.G.M College, Pollachi,

### Privacy, Discovery, and Authentication for the Internet of Things

Privacy, Discovery, and Authentication for the Internet of Things David Wu Joint work with Ankur Taly, Asim Shankar, and Dan Boneh The Internet of Things (IoT) Lots of smart devices, but only useful if

### A New and Efficient Signature on Commitment Values

International Journal of Network Security, Vol.7, No., PP.0 06, July 2008 0 A New and Efficient Signature on Commitment Values Fangguo Zhang,3, Xiaofeng Chen 2,3, Yi Mu 4, and Willy Susilo 4 (Corresponding

### Ensuring Integrity in Cloud Computing via Homomorphic Digital Signatures: new tools and results

Ensuring Integrity in Cloud Computing via Homomorphic Digital Signatures: new tools and results Dario Catalano Dario Fiore Luca Nizzardo University of Catania Italy IMDEA Software Institute Madrid, Spain

### Duality in ABE: Converting Attribute Based Encryption for Dual Predicate and Dual Policy via Computational Encodings

Duality in ABE: Converting Attribute Based Encryption for Dual Predicate and Dual Policy via Computational Encodings Nuttapong Attrapadung, Shota Yamada AIST, Japan @CT-RSA 2015 Our Main Results in One

### Identity based cryptography

Identity based cryptography The case of encryption schemes David Galindo d.galindo@cs.ru.nl Security of Systems Department of Computer Science Radboud Universiteit Nijmegen Identity based cryptography

### Certificate Based Signature Schemes without Pairings or Random Oracles

Certificate Based Signature Schemes without Pairings or Random Oracles p. 1/2 Certificate Based Signature Schemes without Pairings or Random Oracles Joseph K. Liu, Joonsang Baek, Willy Susilo and Jianying

### Chapter 2 TSAS: Third-Party Storage Auditing Service

Chapter 2 TSAS: Third-Party Storage Auditing Service Abstract In cloud storage systems, data owners host their data on cloud servers and users (data consumers) can access the data from cloud servers Due

### Efficient Unlinkable Secret Handshakes for Anonymous Communications

보안공학연구논문지 (Journal of Security Engineering), 제 7권 제 6호 2010년 12월 Efficient Unlinkable Secret Handshakes for Anonymous Communications Eun-Kyung Ryu 1), Kee-Young Yoo 2), Keum-Sook Ha 3) Abstract The technique

### New Efficient Searchable Encryption Schemes from Bilinear Pairings

International Journal of Network Security, Vol.10, No.1, PP.25 31, Jan. 2010 25 New Efficient Searchable Encryption Schemes from Bilinear Pairings Chunxiang Gu and Yuefei Zhu (Corresponding author: Chunxiang

### Overview of Public-Key Cryptography

CS 361S Overview of Public-Key Cryptography Vitaly Shmatikov slide 1 Reading Assignment Kaufman 6.1-6 slide 2 Public-Key Cryptography public key public key? private key Alice Bob Given: Everybody knows

### Secure Network Communication Part II II Public Key Cryptography. Public Key Cryptography

Kommunikationssysteme (KSy) - Block 8 Secure Network Communication Part II II Public Key Cryptography Dr. Andreas Steffen 2000-2001 A. Steffen, 28.03.2001, KSy_RSA.ppt 1 Secure Key Distribution Problem

### New Techniques for Dual System Encryption and Fully Secure HIBE with Short Ciphertexts

New Techniques for Dual System Encryption and Fully Secure HIBE with Short Ciphertexts Allison Lewko 1 and Brent Waters 2 1 University of Texas Austin alewko@cs.utexas.edu 2 University of Texas at Austin

### Asymmetric cryptography in the random oracle model. Gregory Neven IBM Zurich Research Laboratory

Asymmetric cryptography in the random oracle model Gregory Neven IBM Zurich Research Laboratory Overview Provable security: the concept Digital signatures and the Random Oracle Model Public-key encryption

### COM S 687 Introduction to Cryptography October 19, 2006

COM S 687 Introduction to Cryptography October 19, 2006 Lecture 16: Non-Malleability and Public Key Encryption Lecturer: Rafael Pass Scribe: Michael George 1 Non-Malleability Until this point we have discussed

### ON MULTI-AUTHORITY CIPHERTEXT-POLICY ATTRIBUTE-BASED ENCRYPTION

Bull. Korean Math. Soc. 46 (2009), No. 4, pp. 803 819 DOI 10.4134/BKMS.2009.46.4.803 ON MULTI-AUTHORITY CIPHERTEXT-POLICY ATTRIBUTE-BASED ENCRYPTION Sascha Müller, Stefan Katzenbeisser, and Claudia Eckert

### Fuzzy Identity Based Encryption Preliminary Version

Fuzzy Identity Based Encryption Preliminary Version Amit Sahai Brent R. Waters Abstract We introduce a new type of Identity Based Encryption (IBE) scheme that we call Fuzzy Identity Based Encryption. A

### Identity-Based Encryption from the Weil Pairing

Appears in SIAM J. of Computing, Vol. 32, No. 3, pp. 586-615, 2003. An extended abstract of this paper appears in the Proceedings of Crypto 2001, volume 2139 of Lecture Notes in Computer Science, pages

### Hierarchical ID-Based Cryptography

Hierarchical ID-Based Cryptography Craig Gentry 1 and Alice Silverberg 2 1 DoCoMo USA Labs San Jose, CA, USA cgentry@docomolabs-usa.com 2 Department of Mathematics Ohio State University Columbus, OH, USA

### Chosen-Ciphertext Security from Identity-Based Encryption

Chosen-Ciphertext Security from Identity-Based Encryption Ran Canetti 1, Shai Halevi 1, and Jonathan Katz 2 1 IBM T. J. Watson Research Center, Hawthorne, NY. {canetti,shaih}@watson.ibm.com 2 Dept. of

### Verifiable Functional Encryption

Verifiable Functional Encryption Saikrishna Badrinarayanan Vipul Goyal Aayush Jain Amit Sahai Abstract In light of security challenges that have emerged in a world with complex networks and cloud computing,

### Identity-based Encryption with Efficient Revocation

A preliminary version of this paper appears in Proceedings of the 14th ACM Conference on Computer and Communications Security, CCS 2008, ACM Press, 2008. This is the full version. Identity-based Encryption

### Key Policy Attribute-based Proxy Re-encryption and RCCA Secure Scheme

Keying Li, Jianfeng Wang 2, Yinghui Zhang 3, and Hua Ma School of mathematics and statistics, Xidian University, P.R.China likeying88@63.com and ma hua@26.com 2 State Key Laboratory of Integrated Service

### Lecture 13: Message Authentication Codes

Lecture 13: Message Authentication Codes Last modified 2015/02/02 In CCA security, the distinguisher can ask the library to decrypt arbitrary ciphertexts of its choosing. Now in addition to the ciphertexts

### Authentication and Encryption: How to order them? Motivation

Authentication and Encryption: How to order them? Debdeep Muhopadhyay IIT Kharagpur Motivation Wide spread use of internet requires establishment of a secure channel. Typical implementations operate in

### Threshold Identity Based Encryption Scheme without Random Oracles

WCAN 2006 Threshold Identity Based Encryption Scheme without Random Oracles Jin Li School of Mathematics and Computational Science Sun Yat-sen University Guangzhou, P.R. China Yanming Wang Lingnan College

### Message Authentication Code

Message Authentication Code Ali El Kaafarani Mathematical Institute Oxford University 1 of 44 Outline 1 CBC-MAC 2 Authenticated Encryption 3 Padding Oracle Attacks 4 Information Theoretic MACs 2 of 44

### Attributed-based Access Control for Multi-Authority Systems in Cloud Storage

2012 32nd IEEE International Conference on Distributed Computing Systems Attributed-based Access Control for Multi-Authority Systems in Cloud Storage Kan Yang Department of Computer Science City University

### Ballot privacy in elections: new metrics and constructions.

Ballot privacy in elections: new metrics and constructions. Olivier Pereira Université catholique de Louvain Based on joint works with: D. Bernhard, V. Cortier, E. Cuvelier, T. Peters and B. Warinschi

### Simplified Security Notions of Direct Anonymous Attestation and a Concrete Scheme from Pairings

Simplified Security Notions of Direct Anonymous Attestation and a Concrete Scheme from Pairings Ernie Brickell Intel Corporation ernie.brickell@intel.com Liqun Chen HP Laboratories liqun.chen@hp.com March

### 3-6 Toward Realizing Privacy-Preserving IP-Traceback

3-6 Toward Realizing Privacy-Preserving IP-Traceback The IP-traceback technology enables us to trace widely spread illegal users on Internet. However, to deploy this attractive technology, some problems

### Experiments in Encrypted and Searchable Network Audit Logs

Experiments in Encrypted and Searchable Network Audit Logs Bhanu Prakash Gopularam Cisco Systems India Pvt. Ltd Nitte Meenakshi Institute of Technology Email: bhanprak@cisco.com Sashank Dara Cisco Systems

### 1 Construction of CCA-secure encryption

CSCI 5440: Cryptography Lecture 5 The Chinese University of Hong Kong 10 October 2012 1 Construction of -secure encryption We now show how the MAC can be applied to obtain a -secure encryption scheme.

### Verifiable Delegation of Computation over Large Datasets

Verifiable Delegation of Computation over Large Datasets Siavosh Benabbas University of Toronto Rosario Gennaro IBM Research Yevgeniy Vahlis AT&T Cloud Computing Data D Code F Y F(D) Cloud could be malicious

### 1 Public-Key Encryption in Practice

CS 120/CSCI E-177: Introduction to Cryptography Salil Vadhan and Alon Rosen Nov. 16, 2006 Lecture Notes 15: Public-Key Encryption in Practice Recommended Reading. KatzLindell, Sections 9.4, 9.5.3 1 Public-Key

### Digital Signatures. Prof. Zeph Grunschlag

Digital Signatures Prof. Zeph Grunschlag (Public Key) Digital Signatures PROBLEM: Alice would like to prove to Bob, Carla, David,... that has really sent them a claimed message. E GOAL: Alice signs each

### CS 758: Cryptography / Network Security

CS 758: Cryptography / Network Security offered in the Fall Semester, 2003, by Doug Stinson my office: DC 3122 my email address: dstinson@uwaterloo.ca my web page: http://cacr.math.uwaterloo.ca/~dstinson/index.html

### Provably Secure Cryptography: State of the Art and Industrial Applications

Provably Secure Cryptography: State of the Art and Industrial Applications Pascal Paillier Gemplus/R&D/ARSC/STD/Advanced Cryptographic Services French-Japanese Joint Symposium on Computer Security Outline

### Enabling Public Auditing for Secured Data Storage in Cloud Computing

IOSR Journal of Engineering (IOSRJEN) e-issn: 2250-3021, p-issn: 2278-8719 Vol. 3, Issue 5 (May. 2013), V3 PP 01-05 Enabling Public Auditing for Secured Data Storage in Cloud Computing 1 Er.Amandeep Kaur,

### Some Identity Based Strong Bi-Designated Verifier Signature Schemes

Some Identity Based Strong Bi-Designated Verifier Signature Schemes Sunder Lal and Vandani Verma Department of Mathematics, Dr. B.R.A. (Agra), University, Agra-282002 (UP), India. E-mail- sunder_lal2@rediffmail.com,

### Introduction. Chapter 1

Chapter 1 Introduction This is a chapter from version 1.1 of the book Mathematics of Public Key Cryptography by Steven Galbraith, available from http://www.isg.rhul.ac.uk/ sdg/crypto-book/ The copyright

Family Name:... First Name:... Section:... Advanced Cryptography Final Exam July 18 th, 2006 Start at 9:15, End at 12:00 This document consists of 12 pages. Instructions Electronic devices are not allowed.

### Asymmetric Encryption. With material from Jonathan Katz, David Brumley, and Dave Levin

Asymmetric Encryption With material from Jonathan Katz, David Brumley, and Dave Levin Warmup activity Overview of asymmetric-key crypto Intuition for El Gamal and RSA And intuition for attacks Digital

### Boosting Linearly-Homomorphic Encryption to Evaluate Degree-2 Functions on Encrypted Data

Boosting Linearly-Homomorphic Encryption to Evaluate Degree-2 Functions on Encrypted Data Dario Catalano 1 and Dario Fiore 2 1 Dipartimento di Matematica e Informatica, Università di Catania, Italy. catalano@dmi.unict.it

### Improving Privacy and Security in Multi-Authority Attribute-Based Encryption

Improving Privacy and Security in Multi-Authority Attribute-Based Encryption ABSTRACT Melissa Chase Microsoft Research 1 Microsoft Way Redmond, WA 98052, USA melissac@microsoft.com Attribute based encryption

### Improved Proxy Re-Encryption Schemes with Applications to Secure Distributed Storage

Improved Proxy Re-Encryption Schemes with Applications to Secure Distributed Storage Giuseppe Ateniese Kevin Fu Matthew Green Susan Hohenberger Abstract In 1998, Blaze, Bleumer, and Strauss (BBS) proposed

### Technische Universität München Winter term 2010 Theoretische Informatik Dr. M. Luttenberger / A. Gaiser SOLUTION. Cryptography Endterm

Technische Universität München Winter term 2010 Theoretische Informatik Dr. M. Luttenberger / A. Gaiser SOLUTION Cryptography Endterm Last name: First name: Student ID no.: Signature: Code {A,..., Z} 6

### Title Goes Here An Introduction to Modern Cryptography. Mike Reiter

Title Goes Here An Introduction to Modern Cryptography Mike Reiter 1 Cryptography Study of techniques to communicate securely in the presence of an adversary Traditional scenario Goal: A dedicated, private

### Midterm Exam Solutions CS161 Computer Security, Spring 2008

Midterm Exam Solutions CS161 Computer Security, Spring 2008 1. To encrypt a series of plaintext blocks p 1, p 2,... p n using a block cipher E operating in electronic code book (ECB) mode, each ciphertext

### PUBLIC KEY ENCRYPTION

PUBLIC KEY ENCRYPTION http://www.tutorialspoint.com/cryptography/public_key_encryption.htm Copyright tutorialspoint.com Public Key Cryptography Unlike symmetric key cryptography, we do not find historical

### Lecture 9 - Message Authentication Codes

Lecture 9 - Message Authentication Codes Boaz Barak March 1, 2010 Reading: Boneh-Shoup chapter 6, Sections 9.1 9.3. Data integrity Until now we ve only been interested in protecting secrecy of data. However,

### Definitions for Predicate Encryption

Definitions for Predicate Encryption Giuseppe Persiano Dipartimento di Informatica, Università di Salerno, Italy giuper@dia.unisa.it Thursday 12 th April, 2012 Cryptographic Proofs 1 Content Results on

### Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps

Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps Liang Feng Zhang, Reihaneh Safavi-Naini Institute for Security, Privacy and Information Assurance Department

### CS Asymmetric-key Encryption. Prof. Clarkson Spring 2016

CS 5430 Asymmetric-key Encryption Prof. Clarkson Spring 2016 Review: block ciphers Encryption schemes: Enc(m; k): encrypt message m under key k Dec(c; k): decrypt ciphertext c with key k Gen(len): generate

### CIS 6930 Emerging Topics in Network Security. Topic 2. Network Security Primitives

CIS 6930 Emerging Topics in Network Security Topic 2. Network Security Primitives 1 Outline Absolute basics Encryption/Decryption; Digital signatures; D-H key exchange; Hash functions; Application of hash