Cryptography Reference
In-Depth Information
In a hierarchical identity-based encryption scheme, a vector represents the identities.
Let
h
be the maximum height of the HIBE system. Analogous to the IBE scheme, the
PKG sets the public parameters
PP
and the master secret
M
s
.
Analogous to IBE, the HIBE scheme consists of
Set-up
,
Key-Gen
,
Encrypt
,
and
Decrypt.
Set-up
: This takes the security parameters
k
and returns the master private key
and public parameters
PP
. The public parameters include the message space and
the cipher-text space. In addition, the maximal level
h
is also made public.
Key-Gen
: This takes the identity-tuple
id
= (
id
1
,…,
id
j
) for entity
j
and the private
key
d
for the identity (
id
1
,…,
id
j
-1
) and returns the private key
d
id
using
id j
|
-
1
d
.
id j
|
-
1
Encrypt
: This takes the identity
id
I
,
m
M
and public parameters
PP
and
generates the cipher text
C
C
Decrypt
: This algorithm takes the identity
id
I
, cipher text
c
C
, and a private
key
d
id
corresponding
id
I
and returns the message
m
M
or an error message.
4.3.3.1 Gentry-Silverberg HIBE
The Gentry and Silverberg (2002) HIBE is as follows.
Set-up
: This scheme consists of
PP
, where
G
1
is an
additive group of order
q
and
G
2
is a multiplicative group of order
q
. Let
e
be a
bilinear map such that
´
1
=
GG ePQ H H
,
, ,
,
,
,
12
00 1 2
eG G G
. Let
H
1
and
H
2
be cryptographic hash
functions. Let
S
0
be the identity element of
G
1
.
2
2
Root Key-Gen
: Let root PKG pick
Î
*
0
s
Z
and generate
Q
0
=
s
0
P
0
.
q
Lower-Level Key-Gen
: Let entity
E
t
at level
t
(Level
t
) have the ID-tuple (
ID
1
,…,
ID
t
). Let
E
t
's ancestor be at Level
i
, where 1 ≤
i
≤
t
. Let entity
E
t
Level
t
pick a
secret
Î
*
t
s
Z
.
q
Extract
:
E
t
's parent generates the following private key for
E
t
,
t
+
å
S
s
P
s
P
(4.16)
t
--
1
t
1
t
i
-
1
i
=
i
1
where
P
t
=
H
1
(
ID
1
,…,
ID
i
)
G
1
. Furthermore,
E
t
's parent distributes the value
of
Q
i
=
s
i
P
0
for
££-
1
i
t
1
.
Encrypt
: This algorithm encrypts the message
m
M
with the ID-tuple (
ID
1
,…,
ID
t
) as shown below:
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