Cryptography Reference
In-Depth Information
r
CrPrPrPmHg
=
,
,...,
,
Å
(
)
(4.17)
02
t
2
where
•
Î
q
rZ
is the secret picked by entity
t
at Level
t
,
P
i
=
H
1
(
ID
1
,...,
ID
i
)
G
1
for
££-
1
i
t
1
•
=
geQP G
g
=
e
(
Q
0
,
P
1
)
G
2
(,
Î
01
)
2
r
CrPrPrPmHg UU UV
, where
c
C
.
To decrypt
C
, the receiving entity at Level
t
computes
Decrypt
: Let
=
,
,...,
,
Å
(
)
=
,
,...,
,
02
t
2
02
t
æ
ö
÷
ç
÷
ç
÷
ç
÷
ç
÷
eU S
(,
)
ç
÷
ç
÷
Å
0
t
= Î
M
(4.18)
VH
m
ç
÷
2
ç
t
÷
÷
ç
÷
ç
eQ
(
,
U
)
÷
ç
÷
-
ç
i
1
i
÷
ç
è
ø
t
=
2
Although the HIBE is an extension of Boneh-Franklin IBE (discussed in Section
4.3.2.1) to a
t
-level IBE scheme, it still inherits the vulnerabilities of Boneh-Franklin
IBE and is susceptible to chosen cipher-text attack.
4.3.3.2 Dual HIBE: Dual Hierarchical Identity-Based Encryption
The dual HIBE is structured as follows (Gentry and Silverberg 2002).
Assumption
: End users
y
and
z
are close to each other in the hierarchy, with user
y
at level
m
(Level
m
) and user
z
at level
n
(Level
n
). Let there be a common ancestor
at level
i
(Level
i
). Let user
y
have ID-tuple
(
ID
,...,
ID
,...,
ID
)
and user
z
have
y
y
y
1
l
m
ID-tuple
(
ID
,...,
ID
,...,
ID
)
where
(
ID
,...,
ID
)
=
(
ID
,...,
ID
)
.
z
z
z
y
y
z
z
1
l
n
1
l
1
l
Encrypt
: User
y
encrypts a message
m
M
as shown below:
r
CrPrP
=
,
,...,
rPMHg
,
Å
(
)
(4.19)
0
z
z
2
y
+
l
1
n
l
where
eP S
(, )
0
y
g
=
=
e P
(, )
S
y
0
y
m
l
l
(1)
eQ
(
,
P
)
y
y
-
i
i
=+
il
1
P
=
H
(
ID
,....,
ID
)
Î
for
l
+ 1 ≤
i
≤
n
G
z
1
z
z
1
i
1
i
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