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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