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Attribute-based Encryption. (20110705) Threshold ABE (20110719) KP-ABE (20110719) CP-ABE (20111003) v2. Attribute-Based Encryption. [SW05] Threshold ABE [GPSW06] Key-policy ABE [BSW07] Cipher-policy ABE. [SW05] THRESHOLD ABE. Threshold ABE. aka Fuzzy IBE Using biometrics in IBE

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attribute based encryption

Attribute-based Encryption

(20110705) Threshold ABE

(20110719) KP-ABE

(20110719) CP-ABE

(20111003) v2

attribute based encryption1
Attribute-Based Encryption
  • [SW05] Threshold ABE
  • [GPSW06] Key-policy ABE
  • [BSW07] Cipher-policy ABE
threshold abe
Threshold ABE
  • aka Fuzzy IBE
  • Using biometrics in IBE
  • Identity as a set of “attributes”
  • First propose the term of Attribute Based Encryption
setup
Setup
  • Bilinear map: e
    • e: G1× G1-> G2
    • G1 has prime order p
    • g is a generator of G1
key policy abe
Key-policy ABE
  • Ciphertexts are labeled with a set of attributes
  • private keys are associated with access structures that control which ciphertext a user is able to decrypt.
example
Example
  • C1(3,5,6,7)

╳ K1( 1 and 2)

○ K2( 3 or 5 )

○ K3( (1 and 2) or (3 and 7) )

○ K4 ( 3 out of (1,2,3,4,5,6,7) )

╳ K5 ( 2 out of (1,2,5) )

access tree
Access Tree
  • (“child” and “<120cm”) or (2 of (“student”, ”<20”, ”disabled”,))

OR

AND

2 of 3

“<120cm”

“child”

“student”

“<20”

“disabled”

access tree1
Access Tree
  • parent(x): parent of a node x
  • att(x): if x is a leaf node then return the attribute associated with x
access tree3
Access Tree
  • index(x): return node’s index

1

3

2

4

5

6

7

8

setup3
Setup
  • Bilinear map: e
    • e: G1× G1-> G2
    • G1 has prime order p
    • g is a generator of G1
key generation
Key Generation
  • KeyGen(T, MK)

Choose a polynomial qx for each node:q1, q2, q3, … , q8.

degree(qx)= K(x) - 1

degree(q1) = 0

degree(q2) = 1

degree(q3) = 1

degree(q4) = 0

degree(q8) = 0

key generation1
Key Generation

q1(0)=y

q3(0)=q1(3)

q2(0)=q1(2)

q4(0)=q2(4)

q5(0)=q2(5)

q6(0)=q3(6)

q8(0)=q3(8)

q7(0)=q3(7)

slide29

q6(0)=q3(6)

q7(0)=q3(7)

q3(0)=q1(3)

cipher policy abe
Cipher-policy ABE
  • Private keys are labeled with a set S of attributes
  • Ciphertexts are associated with access structures T that control which user is able to decrypt the ciphertext.
example1
Example
  • C1( (1 and 2) or (3 of (4,5,6,7)) )

╳ K1( 1)

○ K2(1, 2)

○ K3(4,5,6)

○ K4 (1,2,4,6,7)

╳ K5 (4,5,8)

setup6
Setup
  • Bilinear map: e
    • e: G1× G1-> G2
    • G1 has prime order p
    • g is a generator of G1
setup7
Setup
  • U = {a1=child, a2=<120cm, … ,an }
    • U is the set of all attributes
  • H: U -> G1
encryption3
Encryption
  • q1(0)=s

q3(0)=q1(3)

q2(0)=q1(2)

q4(0)=q2(4)

q5(0)=q2(5)

q6(0)=q3(6)

q8(0)=q3(8)

q7(0)=q3(7)

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