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

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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

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[SW05] THRESHOLD ABE 3

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

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Threshold ABE 5

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

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Setup 7

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Encryption 9

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Extract 10

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Decryption 11

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Decryption 12

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[GPSW06] KEY-POLICY ABE 13

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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

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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

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

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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

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Access Tree 18

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

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

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Setup 21

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Setup 22

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Encryption 23

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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

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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

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Key Generation 26

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Decryption 27

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

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[BSW07] CIPHER-POLICY ABE 30

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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

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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

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

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

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Setup 35

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Encryption 36

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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

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Encryption 38

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Key Generation 39

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Decryption 40

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