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
Search WWH ::




Custom Search