dating + big data user . . . . . . . . dating + big data - PowerPoint PPT Presentation

encrypted computation from lattices Hoeteck Wee ENS, Paris . . . . . . . .

dating + big data user . . . . . . . .

dating + big data user profile limit access? . . . . . . . .

dating + big data user profile tall ∧ dark ∧ handsome . . . . . . . .

dating + big data user profile (tall ∧ dark ∧ handsome) ∨ (phd ∧ cs) . . . . . . . .

dating + big data me tall dark user profile handsome cs (tall ∧ dark ∧ handsome) ∨ (phd ∧ cs) math phd . . . . . . . .

dating + big data me tall dark user profile handsome cs (tall ∧ dark ∧ handsome) ∨ (phd ∧ cs) math phd . . . . . . . .

dating + big data me tall dark user handsome cs (tall ∧ dark ∧ handsome) ∨ (phd ∧ cs) math phd . . . . . . . .

dating + big data me tall dark user profile handsome cs (tall ∧ dark ∧ handsome) ∨ (phd ∧ cs) math phd . . . . . . . .

dating + big data me tall dark user profile handsome cs (tall ∧ dark ∧ handsome) ∨ (phd ∧ cs) math phd collusion . . . . . . . .

attribute-based encryption [ GPSW06,SW05 ] sender receiver M f , M x , sk x learns M ⇔ f ( x ) = 1 . . . . . . . .

attribute-based encryption [ GPSW06,SW05 ] + sender receiver receiver M f , M x , sk x x ′ , sk x ′ learns M ⇔ f ( x ) = 1 security against collusions . . . . . . . .

attribute-based encryption [ GPSW06,SW05 ] + sender receiver receiver M f , M x , sk x x ′ , sk x ′ learns M ⇔ f ( x ) = 1 2001 – 2013. shallow circuits [ BF01, CHK04, BB04, GPSW06, W09, LW10, LOSTW10, OT10, ... ] . . . . . . . .

attribute-based encryption [ GPSW06,SW05 ] + sender receiver receiver M f , M x , sk x x ′ , sk x ′ learns M ⇔ f ( x ) = 1 2013. all circuits from LWE [ Gorbunov Vaikuntanathan W 13, Boneh Gentry Gorbunov Halevi Nikolaenko Segev Vaikuntanathan Vinayagamurthy 14 ] . . . . . . . .

attribute-based encryption (I) M cs phd phd ∧ cs cs msc bio phd . . . . . . . .

attribute-based encryption (I) + M M cs phd phd ∧ cs cs msc bio phd . . . . . . . .

attribute-based encryption (I) M cs phd phd ∧ cs cs msc + bio phd collusion . . . . . . . .

attribute-based encryption (I) R cs , R phd M cs phd phd ∧ cs R cs , R msc cs msc R bio , R phd bio phd . . . . . . . .

attribute-based encryption (I) M ⊕ R cs ⊕ R phd R cs , R phd M cs phd phd ∧ cs R cs , R msc cs msc R bio , R phd bio phd . . . . . . . .

attribute-based encryption (I) + M M ⊕ R cs ⊕ R phd R cs , R phd M cs phd phd ∧ cs R cs , R msc cs msc R bio , R phd bio phd . . . . . . . .

attribute-based encryption (I) M ⊕ R cs ⊕ R phd R cs , R phd M cs phd phd ∧ cs + R cs , R msc cs msc + R bio , R phd bio phd . . . . . . . .

attribute-based encryption (I) M ⊕ R cs ⊕ R phd R cs , R phd M cs phd phd ∧ cs R cs , R msc cs msc + R bio , R phd bio phd collusion . . . . . . . .

attribute-based encryption (I) M M ⊕ R cs ⊕ R phd R cs , R phd M cs phd phd ∧ cs mix and match R cs , R msc cs msc + R bio , R phd bio phd collusion . . . . . . . .

attribute-based encryption (I) M M ⊕ R cs ⊕ R phd R cs , R phd M cs phd phd ∧ cs mix and match R cs , R msc ⇒ cs msc + insecure against collusions R bio , R phd bio phd collusion . . . . . . . .

attribute-based encryption (I) M ⊕ R cs ⊕ R phd R cs , R phd M Key Idea. [ GVW13 ] cs phd strings R → functions φ ( · ) phd ∧ cs one-use → many-use mix and match R cs , R msc cs msc R bio , R phd bio phd . . . . . . . .

attribute-based encryption (I) R cs , R phd M φ cs ( · ) , φ phd ( · ) cs phd phd ∧ cs R cs , R msc φ cs ( · ) , φ msc ( · ) cs msc R bio , R phd φ bio ( · ) , φ phd ( · ) bio phd . . . . . . . .

attribute-based encryption (I) φ cs ( s ) , φ phd ( s ) R cs , R phd M cs phd phd ∧ cs φ cs ( t ) , φ msc ( t ) R cs , R msc cs msc R bio , R phd φ bio ( u ) , φ phd ( u ) bio phd . . . . . . . .

attribute-based encryption (I) + M φ cs ( s ) , φ phd ( s ) R cs , R phd M cs phd phd ∧ cs φ cs ( t ) , φ msc ( t ) R cs , R msc cs msc R bio , R phd φ bio ( u ) , φ phd ( u ) bio phd . . . . . . . .

attribute-based encryption (I) + M φ cs ( s ) , φ phd ( s ) R cs , R phd M cs phd φ cs ( s ′ ) , φ phd ( s ′ ) phd ∧ cs φ cs ( t ) , φ msc ( t ) R cs , R msc cs msc R bio , R phd φ bio ( u ) , φ phd ( u ) bio phd . . . . . . . .

attribute-based encryption (I) φ cs ( s ) , φ phd ( s ) R cs , R phd M cs phd phd ∧ cs φ cs ( t ) , φ msc ( t ) φ cs ( t ) , φ msc ( t ) R cs , R msc cs msc mix and match + R bio , R phd φ bio ( u ) , φ phd ( u ) φ bio ( u ) , φ phd ( u ) bio phd collusion . . . . . . . .

attribute-based encryption (I) φ cs ( s ) , φ phd ( s ) R cs , R phd M theorem. [ GVW13 ] cs phd secure against collusions phd ∧ cs works for general circuits φ cs ( t ) , φ msc ( t ) φ cs ( t ) , φ msc ( t ) R cs , R msc cs msc mix and match + R bio , R phd φ bio ( u ) , φ phd ( u ) φ bio ( u ) , φ phd ( u ) bio phd collusion . . . . . . . .

attribute-based encryption (I) φ cs φ phd theorem. [ GVW13 ] ∧ secure against collusions works for general circuits φ 1 φ 2 ∨ φ 3 φ 4 ∧ φ out . . . . . . . .

A i x f small H f x lemma II . A x G A n x n G H f x A f f x G attribute-based encryption (II) receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 . . . . . . . .

attribute-based encryption (II) receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 ∀ A i , ∀ x , ∀ f , ∃ small H f , x lemma II ∗ . [ A 1 − x 1 G | · · · | A n − x n G ] · H f , x = A f − f ( x ) G . . . . . . . .

A attribute-based encryption (II) A 1 , . . . , A n , P receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 ∀ A i , ∀ x , ∀ f , ∃ small H f , x lemma II ∗ . [ A 1 − x 1 G | · · · | A n − x n G ] · H f , x = A f − f ( x ) G . . . . . . . .

A attribute-based encryption (II) A 1 , . . . , A n , P receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 s [ A 1 − x 1 G | · · · | A n − x n G ] + e , sP + M ∀ A i , ∀ x , ∀ f , ∃ small H f , x lemma II ∗ . [ A 1 − x 1 G | · · · | A n − x n G ] · H f , x = A f − f ( x ) G . . . . . . . .

A attribute-based encryption (II) A 1 , . . . , A n , P A f · sk f = P receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 s [ A 1 − x 1 G | · · · | A n − x n G ] + e , sP + M ∀ A i , ∀ x , ∀ f , ∃ small H f , x lemma II ∗ . [ A 1 − x 1 G | · · · | A n − x n G ] · H f , x = A f − f ( x ) G . . . . . . . .

A attribute-based encryption (II) A 1 , . . . , A n , P A f · sk f = P receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 s [ A 1 − x 1 G | · · · | A n − x n G ] + e , sP + M ∀ A i , ∀ x , ∀ f , ∃ small H f , x lemma II ∗ . [ A 1 − x 1 G | · · · | A n − x n G ] · H f , x = A f − f ( x ) G correctness. f ( x ) = 0 ⇒ learns M . . . . . . . .

A sk f attribute-based encryption (II) A 1 , . . . , A n , P A f · sk f = P receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 s [ A 1 − x 1 G | · · · | A n − x n G ] + e , sP + M ∀ A i , ∀ x , ∀ f , ∃ small H f , x lemma II ∗ . [ A 1 − x 1 G | · · · | A n − x n G ] · H f , x = A f − f ( x ) G correctness. f ( x ) = 0 ⇒ learns M s [ A 1 − x 1 G | · · · | A n − x n G ] H f , x = s ( A f − f ( x ) G ) . . . . . . . .

A sk f attribute-based encryption (II) A 1 , . . . , A n , P A f · sk f = P receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 s [ A 1 − x 1 G | · · · | A n − x n G ] + e , sP + M ∀ A i , ∀ x , ∀ f , ∃ small H f , x lemma II ∗ . [ A 1 − x 1 G | · · · | A n − x n G ] · H f , x = A f − f ( x ) G correctness. f ( x ) = 0 ⇒ learns M s [ A 1 − x 1 G | · · · | A n − x n G ] H f , x = sA f . . . . . . . .

A attribute-based encryption (II) A 1 , . . . , A n , P A f · sk f = P receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 s [ A 1 − x 1 G | · · · | A n − x n G ] + e , sP + M ∀ A i , ∀ x , ∀ f , ∃ small H f , x lemma II ∗ . [ A 1 − x 1 G | · · · | A n − x n G ] · H f , x = A f − f ( x ) G correctness. f ( x ) = 0 ⇒ learns M s [ A 1 − x 1 G | · · · | A n − x n G ] H f , x · sk f = sA f · sk f . . . . . . . .

A attribute-based encryption (II) A 1 , . . . , A n , P A f · sk f = P receiver sender M x , M f , sk f learns M ⇔ f ( x ) = 0 s [ A 1 − x 1 G | · · · | A n − x n G ] + e , sP + M ∀ A i , ∀ x , ∀ f , ∃ small H f , x lemma II ∗ . [ A 1 − x 1 G | · · · | A n − x n G ] · H f , x = A f − f ( x ) G correctness. f ( x ) = 0 ⇒ learns M s [ A 1 − x 1 G | · · · | A n − x n G ] H f , x · sk f = sP . . . . . . . .