Unbounded ABE via Bilinear Entropy Expansion, Revisited Jie Chen - PowerPoint PPT Presentation

Unbounded ABE via Bilinear Entropy Expansion, Revisited Jie Chen Junqing Gong Lucas Kowalczyk Hoeteck Wee ECNU ENS de Lyon Columbia University ENS & CNRS

attribute-based encryption (ABE) [SW05, GPSW06] 1

attribute-based encryption (ABE) [SW05, GPSW06] !"# !$# 2

attribute-based encryption (ABE) [SW05, GPSW06] $%" $!" !" # (’CS’ and ‘PhD’) or ‘Professor’ !" & ’CS’ and ‘PhD’ !" ' ’EE’ and ‘Professor’ 3

attribute-based encryption (ABE) [SW05, GPSW06] $%" $!" !" # (’CS’ and ‘PhD’) or ‘Professor’ !" & enc($) ’CS’ and ‘PhD’ (’CS’, ’Professor’) !" ' ’EE’ and ‘Professor’ 4

attribute-based encryption (ABE) [SW05, GPSW06] (’CS’ and ‘PhD’) or ‘Professor’ ’CS’ and ‘PhD’ (’CS’, ’Professor’) ’EE’ and ‘Professor’ 5

attribute-based encryption (ABE) [SW05, GPSW06] (’CS’ and ‘PhD’) or ‘Professor’ ’CS’ and ‘PhD’ (’CS’, ’Professor’) ’EE’ and ‘Professor’ 6

attribute-based encryption (ABE) [SW05, GPSW06] (’CS’ and ‘PhD’) or ‘Professor’ ’CS’ and ‘PhD’ (’CS’, ’Professor’) collusion ’EE’ and ‘Professor’ 7

attribute-based encryption (ABE) [SW05, GPSW06] &'" &!" !" # (’CS’ and ‘PhD’) or ‘Professor’ !" $ enc(&) ’CS’ and ‘PhD’ (’CS’, ’Professor’) !" % ’EE’ and ‘Professor’ 8

attribute-based encryption (ABE) [SW05, GPSW06] &'" &!" !" # (’CS’ and ‘PhD’) or ‘Professor’ !" $ enc(&) ’CS’ and ‘PhD’ (’CS’, ’Professor’) !" % all attributes: [.] = {1, 2, ⋯ , .} ’EE’ and ‘Professor’ 9

attribute-based encryption (ABE) [SW05, GPSW06] -., -+, +, " ! " # = true +, % enc(-) ! % # = false # ⊆ [)] +, & ! & # = false all attributes: [)] = {1, 2, ⋯ , )} 10

ABE !"# = % & bounded !"# + , ' = true + - ' = false ' ⊆ [&] + . ' = false all attributes: [&] = {1, 2, ⋯ , &} 11

unbounded ABE )*+ = , - bounded unbounded !"# = %(') [ LewkoWaters11 ] )*+ 2 3 . = true 2 4 . = false . ⊆ [-] 2 5 . = false all attributes: [-] = {1, 2, ⋯ , -} 12

state of the art • L ewko W aters11 efficient (bilinear) groups prime-order - asymmetric • O kamoto T akashima12 • R ouselakis W aters13 adaptive security • Att rapadung14 adversary can choose the target at any time • K owalczyk L ewko15 • Att rapadung16 standard assumption • A grawal C hase17 ! -Lin, DLin and more - without random oracle 13

state of the art • L ewko W aters11 efficient (bilinear) groups prime-order - asymmetric • O kamoto T akashima12 • R ouselakis W aters13 adaptive security • Att rapadung14 adversary can choose the target at any time • K owalczyk L ewko15 • Att rapadung16 static assumption • A grawal C hase17 ! -Lin, DLin and more 14

state of the art efficient (bilinear) groups prime-order - asymmetric • O kamoto T akashima12 adaptive security adversary can choose the target at any time static assumption ! -Lin, DLin and more 15

this work new and simpler unbounded ABE schemes - more efficient : 40% shorter ciphertext/key; or - more expressive : arithmetic span program 16

this work new and simpler unbounded ABE schemes � more efficient : 40% shorter ciphertext/keyor - more expressive : arithmetic span program 17

this work new and simpler unbounded ABE schemes � more efficient : 40% shorter ciphertext/key � more expressive : arithmetic span program 18

this work new and simpler unbounded ABE schemes � more efficient : 40% shorter ciphertext/key � more expressive : arithmetic span program unbounded ABE compiler bounded ABE scheme 19

this work new and simpler unbounded ABE schemes � more efficient : 40% shorter ciphertext/key � more expressive : arithmetic span program unbounded ABE compiler bounded ABE scheme entropy expansion lemma proof 20

this work new and simpler unbounded ABE schemes � more efficient : 40% shorter ciphertext/key � more expressive : arithmetic span program unbounded ABE compiler bounded ABE [ LOSTW10 ] � scheme [ IW14 ] � 21

compiler & lemma unbounded ABE compiler bounded ABE entropy expansion lemma 22

compiler & lemma unbounded ABE compiler bounded ABE entropy expansion lemma bilinear group of composite order ! " ! # 23

compiler & lemma unbounded ABE compiler bounded ABE entropy expansion lemma bilinear group of composite order $ % $ & ! ℍ ! " 24

compiler & lemma unbounded ABE compiler bounded ABE entropy expansion lemma bilinear group of composite order ( ) ( * #: ! × ℍ ! " ⟶ 25

compiler & lemma unbounded ABE compiler bounded ABE entropy expansion lemma bilinear group of composite order + , + - #: ! × ℍ ! " ⟶ ⋅ ( ) ( * .1 -subgroup .2 -subgroup 26

compiler & lemma unbounded ABE compiler bounded ABE entropy expansion lemma bilinear group of composite order + , + - #: ! × ℍ ! " ⟶ ⋅ ⋅ ( ) ( * ℎ ) ℎ * .1 -subgroup .2 -subgroup .1 -subgroup .2 -subgroup 27

compiler & lemma unbounded ABE compiler bounded ABE 28

compiler & lemma unbounded ABE compiler bounded ABE * - ) * + , … , ' ( ! "#$ = ( ' ( , ' ( # ( -subgroup 29

compiler & lemma unbounded ABE compiler bounded ABE * - ) * + , … , ' ( ! "#$ = ( ' ( , ' ( /* 0 , ' ( / ' ( ct 1 ∈ 3 # ( -subgroup 30

compiler & lemma unbounded ABE compiler bounded ABE * - ) * + , … , ' ( ! "#$ = ( ' ( , ' ( /* 0 , ' ( / ' ( ct 1 ∈ 3 # ( -subgroup 31

compiler & lemma unbounded ABE compiler bounded ABE * - ) * + , … , ' ( ! "#$ = ( ' ( , ' ( /* 0 , ' ( / ' ( ct 3 ∈ 5 2* 0 , ℎ ( 2 ℎ ( sk 3 ∈ 5 # ( -subgroup 32

compiler & lemma unbounded ABE compiler bounded ABE / + ) * - ) / 0 , ' ( * + , … , ' ( ! "#$ = ( ' ( , ' ( "#$ = ( ' ( , ' ( 4* 5 , ' ( 4 ' ( ct 1 ∈ 3 7* 5 , ℎ ( 7 ℎ ( sk 1 ∈ 3 # ( -subgroup # ( -subgroup 33

compiler & lemma unbounded ABE compiler bounded ABE / + ) * - ) / 0 , ' ( * + , … , ' ( ! "#$ = ( ' ( , ' ( "#$ = ( ' ( , ' ( 1 2 + 4 5 1 ( ⟻ 7 8 ;* < , ' ( ; ' ( ct 4 ∈ : >* < , ℎ ( > ℎ ( sk 4 ∈ : [ LewkoWaters11 ] # ( -subgroup # ( -subgroup 34

compiler & lemma unbounded ABE compiler bounded ABE / + ) * - ) / 0 , ' ( * + , … , ' ( ! "#$ = ( ' ( , ' ( "#$ = ( ' ( , ' ( : ; + 1 = : ( ⟻ ? 6 4 / 0 56⋅/ + , ' ( 4* @ , ' ( 4 4 ' ( ct 1 ∈ 3 1 ∈ 3 ' ( 9 / 0 56⋅/ + , ℎ ( 9* @ , ℎ ( 9 9 1 ∈ 3 ℎ ( sk ℎ ( 1 ∈ 3 [ LewkoWaters11 ] # ( -subgroup # ( -subgroup 35

compiler & lemma unbounded ABE bounded ABE entropy expansion lemma / + ) * - ) / 0 , ' ( * + , … , ' ( ! "#$ = ( ' ( , ' ( "#$ = ( ' ( , ' ( 4 / 0 56⋅/ + , ' ( 4* : , ' ( 4 4 ' ( ct 1 ∈ 3 1 ∈ 3 ' ( 9 / 0 56⋅/ + , ℎ ( 9* : , ℎ ( 9 9 1 ∈ 3 ℎ ( sk ℎ ( 1 ∈ 3 # ( -subgroup # ( -subgroup 36

compiler & lemma unbounded ABE bounded ABE entropy expansion lemma 0 , ) + . ) 0 1 , ( ) + , , … , ( ) " #$% = ( ( ) , ( ) #$% = ( ( ) , ( ) ≈ 5 0 1 67⋅0 , , ( ) 5+ ; , ( ) 5 5 ( ) ct 2 ∈ 4 2 ∈ 4 ( ) : 0 1 67⋅0 , , ℎ ) :+ ; , ℎ ) : : 2 ∈ 4 ℎ ) sk ℎ ) 2 ∈ 4 $ ) -subgroup $ ) -subgroup 37

compiler & lemma unbounded ABE bounded ABE entropy expansion lemma 0 , ) + . ) 0 1 , ( ) + , , … , ( ) " #$% = ( ( ) , ( ) #$% = ( ( ) , ( ) ≈ / 5 0 1 67⋅0 , , ( ) 5+ ; , ( ) 5 5 ( ) ct 2 ∈ 4 2 ∈ 4 ( ) : 0 1 67⋅0 , , ℎ ) :+ ; , ℎ ) : : 2 ∈ 4 ℎ ) sk ℎ ) 2 ∈ 4 $ ) -subgroup $ ) -subgroup 38

compiler & lemma unbounded ABE bounded ABE entropy expansion lemma 0 2 ) 0 1 , & / +$, = ( & / , & / ' 0 1 45⋅0 2 , & / '( ) , & % ' ' & % ct ! ∈ # ! ∈ # & / 8 0 1 45⋅0 2 , ℎ / 8( ) , ℎ % 8 8 ! ∈ # ℎ % sk ℎ / ! ∈ # $ / -subgroup $ % -subgroup 39

compiler & lemma unbounded ABE bounded ABE entropy expansion lemma 2 4 ) 2 4 ) 2 3 , ( 1 2 3 , ( 1 -$. = ( ( 1 , ( 1 -$. = ( ( 1 , ( 1 ≈ ⋅ ) 2 3 67⋅2 4 , ( 1 ) 2 3 67⋅2 4 , ( 1 )* + , ( % ) ) ) ( % ct ! ∈ # ! ∈ # ( 1 ( 1 ! ∈ # 9 2 3 67⋅2 4 , ℎ 1 9 2 3 67⋅2 4 , ℎ 1 9* + , ℎ % 9 9 9 ! ∈ # ℎ % sk ℎ 1 ℎ 1 ! ∈ # ! ∈ # $ 1 -subgroup $ 1 -subgroup $ % -subgroup 40

compiler & lemma unbounded ABE bounded ABE entropy expansion lemma 2 4 ) 2 4 ) 2 3 , ( 1 2 3 , ( 1 -$. = ( ( 1 , ( 1 -$. = ( ( 1 , ( 1 ≈ ⋅ ) 2 3 67⋅2 4 , ( 1 ) 2 3 67⋅2 4 , ( 1 )* + , ( % ) ) ) ( % ct ! ∈ # ! ∈ # ( 1 ( 1 ! ∈ # 9 2 3 67⋅2 4 , ℎ 1 9 2 3 67⋅2 4 , ℎ 1 9* + , ℎ % 9 9 9 ! ∈ # ℎ % sk ℎ 1 ℎ 1 ! ∈ # ! ∈ # $ 1 -subgroup $ 1 -subgroup $ % -subgroup dual system method [Waters09] 41