Attribute-based Encryption

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Presentation transcript:

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 Identity as a set of “attributes” First propose the term of Attribute Based Encryption

Threshold ABE

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

Setup

Setup

Encryption

Extract

Decryption

Decryption

[GPSW06] 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 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 (“child” and “<120cm”) or (2 of (“student”, ”<20”, ”disabled”,)) OR AND 2 of 3 “child” “<120cm” “student” “<20” “disabled”

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 Tree

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

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

Setup

Setup

Encryption

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

Key Generation

Decryption

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

[BSW07] 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.

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

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

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

Setup

Encryption

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)

Encryption

Key Generation α, β

Decryption