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

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

3. [SW05] THRESHOLD ABE

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

5. Threshold ABE

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

7. Setup

8. Setup

9. Encryption

10. Extract

11. Decryption

12. Decryption

13. [GPSW06] KEY-POLICY ABE

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.

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) )

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

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

18. Access Tree

19. Access Tree
index(x): return node’s index 1 3 2 4 5 6 7 8

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

21. Setup

22. Setup

23. Encryption

24. 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

25. Key Generation q1(0)=y q2(0)=q1(2) q3(0)=q1(3) q4(0)=q2(4) q5(0)=q2(5)

26. Key Generation

27. Decryption

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

30. [BSW07] CIPHER-POLICY ABE

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.

32. Example C1( (1 and 2) or (3 of (4,5,6,7)) ) ╳ K1( 1) ○ K2(1, 2)

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

34. Setup U = {a1=child, a2=<120cm, … ,an } H: U -> G1
U is the set of all attributes
H: U -> G1

35. Setup

36. Encryption

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

38. Encryption

39. Key Generation
α, β

40. Decryption