Efficient (Hierarchical) Inner Product
Encryption Tightly Reduced from the
Decisional Linear Assumption
2012 / 8 / 21
Tatsuaki Okamoto ( NTT ),
Katsuyuki Takashima ( Mitsubishi Electric )).
T appear in
To
i IEICE Trans.
T
Fundamentals
F d
t l
1
Predicate Encryption
Master p
public-key:
y p
pk
Master secret-key: sk
P bli h
Publish
pk
Authority
Predicate f
Bob
c = Enc( pk, x, m )
（encryption for
attribute x and
plaintext m）
Hiding
gm
and x
Secret-key
f f ( skkf )
for
Alice
c
m = Dec(skf , c)
（can be decrypted
iff f( x ) = 1 ）
2
Inner Product Encryption ( IPE ) [KSW08]
3
Fully Attribute-Hiding Security of IPE
Challenger
No additional information on
is revealed to anyone,
(even to any person with a matching key
, i.e.,
)
4
Fully Attribute-Hiding Security of IPE
selective game
Challenger
No additional information on
is revealed to anyone,
(even to any person with a matching key
, i.e.,
)
5
Previous Works ( Pairing-Based IPE )
• [ KSW08, LOS+10, OT09, OT10, P11 ] : Aim at better security,
e.g., adaptive security, fully-attribute-hiding,
weaker (standard) assumptions
• [ OT12 ] : Adaptively secure and fully attribute-hiding IPE
under the DLIN assumption
From a practical point, the performance is not so satisfactory,
elements of ,
e.g., ciphertext includes
the security reduction is not tight.
Our Result
Proposed IPE
 Fully-attribute-hiding
F ll tt ib t hidi andd selectively
l ti l secure from
f
DLIN,
DLIN
 Almost the shortest ciphertext among existing attributeie
elements of
and 1 element of
hiding IPEs,
IPEs i.e.,
 The security reduction is ( almost ) tight.
,
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Comparison
highest
securityy !
dimension of attribute vector
fully-AH
fully
AH
the maximum number of key-queries
tight reduction from DLIN
size of an element of
shortest CT
AH : attribute-hiding
PK SK
PK,
SK, CT : public
bli key,
k secrett key,
k ciphertext
i h t t
GSD, DSP, DBDH : general subgroup decision, decisional subspace problem,
decisional bilinear Diffie-Hellman
7
Thank
a You
ou !
8