Cryptography Reference
In-Depth Information
Alice
Bob
PP
GG qenH H PP
,
,
, ,
,
,
,
,
12
1 2
pub
Let m א M and
r
*
q
CUV PmHg
,
,
(
r
id
)
2
*
2
where
g
eQ
(
,
P
)
G
id
id
pub
C
M
VHedU m
2 ((
, ))
ID
Figure 4.11. Boneh-Franklin IBE Basic Scheme
Å
=
VHedU
2 ((
, ))
m
(4.8)
ID
4.3.2.2 Boneh and Boyen IBE Scheme Without Random Oracles
Boneh and Boyen's IBE scheme belongs to the family of “commutative blinding”
schemes (Boneh and Boyen 2004). Compared to the Boneh and Franklin IBE scheme,
identity-based crypto-systems based on commutative blinding schemes hash map the
identity to an integer rather than a point on the elliptic curve. Consequently, such
schemes are faster than the full-domain hash schemes, as they avoid modular exponen-
tiation. In this section, we discuss the basic Boneh-Boyen IBE scheme (Figure 4.12).
This scheme consists of Set-up , Key-Gen , Encrypt , and Decrypt .
Alice
Bob
PP
GG qeH H PPPv
,
,
, ,
,
,
,
,
,
1
T
3
4
1
2
3
Q id = H 3 ( id )
k = v s א G T
c = m ْ Ͷ ሺሻ and
C 0 = sP and
C 1 = Q id ( sP 1 ) + sP 3
C = ( c , C 0 , C 1 )
eC D
(, )
(, )
k
00
eC D
11
mc Hk
4 ()
Figure 4.12. Boneh-Boyen Basic IBE Scheme
 
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