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Attribute-based Encryption (20110705) Threshold ABE (20110719) KP-ABE (20110719) CP-ABE (20111003) v2 1.

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Presentation on theme: "Attribute-based Encryption (20110705) Threshold ABE (20110719) KP-ABE (20110719) CP-ABE (20111003) v2 1."— Presentation transcript:

1 Attribute-based Encryption ( ) Threshold ABE ( ) KP-ABE ( ) CP-ABE ( ) v2 1

2 Attribute-Based Encryption  [SW05] Threshold ABE [SW05] Threshold ABE  [GPSW06] Key-policy ABE [GPSW06] Key-policy ABE  [BSW07] Cipher-policy ABE [BSW07] Cipher-policy ABE 2

3 [SW05] THRESHOLD ABE 3

4 Threshold ABE  aka Fuzzy IBE  Using biometrics in IBE  Identity as a set of “attributes”  First propose the term of Attribute Based Encryption 4

5 Threshold ABE  5

6 Setup  Bilinear map: e  e: G1× G1 -> G2  G1 has prime order p  g is a generator of G1 6

7 Setup  7

8  8

9 Encryption  9

10 Extract  10

11 Decryption  11

12 Decryption  12

13 [GPSW06] KEY-POLICY ABE 13

14 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. 14

15 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) ) 15

16 Access Tree  (“child” and “<120cm”) or (2 of (“student”, ”<20”, ”disabled”,)) OR AND 2 of 3 “student” “disabled”“<20” “<120cm” “child” 16

17 Access Tree  parent(x): parent of a node x  att(x): if x is a leaf node then return the attribute associated with x 17

18 Access Tree  18

19 Access Tree  index(x): return node’s index

20 Setup  Bilinear map: e  e: G1× G1 -> G2  G1 has prime order p  g is a generator of G1 20

21 Setup  21

22 Setup  22

23 Encryption  23

24 Key Generation  KeyGen(T, MK) Choose a polynomial q x for each node:q1, q2, q3, …, q8. degree(q x ) = K(x) - 1 degree(q1) = 0 degree(q2) = 1 degree(q3) = 1 degree(q4) = 0 ︴ degree(q8) = 0 24

25 Key Generation q1(0)=y q2(0)=q1(2) q3(0)=q1(3) q4(0)=q2(4)q5(0)=q2(5)q6(0)=q3(6) q7(0)=q3(7) q8(0)=q3(8) 25

26 Key Generation  26

27 Decryption  27

28 28

29 q6(0)=q3(6) q7(0)=q3(7) q3(0)=q1(3) 29

30 [BSW07] CIPHER-POLICY ABE 30

31 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. 31

32 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) 32

33 Setup  Bilinear map: e  e: G1× G1 -> G2  G1 has prime order p  g is a generator of G1 33

34 Setup  U = {a 1 =child, a 2 =<120cm, …,a n }  U is the set of all attributes  H: U -> G1 34

35 Setup  35

36 Encryption  36

37 Encryption q1(0)=s q2(0)=q1(2) q3(0)=q1(3) q4(0)=q2(4)q5(0)=q2(5)q6(0)=q3(6) q7(0)=q3(7) q8(0)=q3(8) 37

38 Encryption  38

39 Key Generation  39

40 Decryption  40

41  41

42  42


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