Cryptography Reference
In-Depth Information
4.3.2.1 Boneh and Franklin IBE Scheme
Boneh and Franklin explain the basic idea of the identity-based encryption scheme
through a simple scheme named BasicIdent (Boneh and Franklin 2001). This scheme
uses a shared secret that can be calculated by both the sender and the receiver of a mes-
sage to encrypt a plain text. Here we describe the basic scheme, which is secure against
chosen plain-text attacks and adaptive chosen-identity attacks, while the full Boneh-
Franklin IBE (Boneh and Franklin 2001) is resistant to chosen cipher-text attacks and
adaptive chosen-identity attacks.
The BasicIdent scheme consists of Set-up , Key-Gen , Encrypt , and Decrypt.
Set-up : Let k Z and the master secret M s Z q . Let G be a bilinear Diffie-
Hellman (BDH) parameter generator. Let G 1 , G 2 be two groups of order q and
let P  G 2 be a random generator. Let there exist a bilinear map e such that
e : G 1 × G 1 G 2
(4.2)
Let P pub = M s P .
Let the cryptographic hash functions be defined as
*
*
H
:{0,1}
G
(4.3)
1
1
n
HG
:
{0,1}
for so e
n
(4.4)
2
2
Let the message space M = {0,1} n and the cipher text C = G 1 * × {0,1} n .
Hence, the system parameters =
PP
GG qenH H PP
,
, , , ,
,
,
,
.
12
1 2
pub
Key-Gen : The algorithm computes
*
1
id QHidG
()
(4.5)
1
where id I and the private key corresponding to identity id I is defined as
=
d
MQ
(4.6)
id
s
id
Encrypt : This algorithm chooses a random integer r Z q and encrypts a message
m M to generate the cipher text
==Å
r
id
= Î *
CUV rPmHg
,
,
(
)
where
g
e QP
(
,
)
G
(4.7)
2
id
id
pub
2
Decrypt : Let id be the public key used to generate the cipher text C C , where
the private key Î 1 ,
id dG then the algorithm decrypts C to generate m M as
shown below (Figure 4.11).
Search WWH ::




Custom Search