Attribute based encryption
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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

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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


Sw05 threshold abe

[SW05] THRESHOLD 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


Threshold abe1

Threshold ABE


Setup

Setup

  • Bilinear map: e

    • e: G1× G1-> G2

    • G1 has prime order p

    • g is a generator of G1


Setup1

Setup


Setup2

Setup


Encryption

Encryption


Extract

Extract


Decryption

Decryption


Decryption1

Decryption


Gpsw06 key policy abe

[GPSW06] KEY-POLICY ABE


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 tree2

Access Tree


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


Setup4

Setup


Setup5

Setup


Encryption1

Encryption


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)


Key generation2

Key Generation


Decryption2

Decryption


Attribute based encryption

q6(0)=q3(6)

q7(0)=q3(7)

q3(0)=q1(3)


Bsw07 cipher policy abe

[BSW07] CIPHER-POLICY ABE


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


Setup8

Setup


Encryption2

Encryption


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)


Encryption4

Encryption


Key generation3

Key Generation


Decryption3

Decryption


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