Cryptography Reference
In-Depth Information
Then, the probability that no key is shared between any two rings is t 2 / t 1 . Hence, the
probability p is
2
t
((
Q
-
m
)!)
=- =-
2
p
1
1
(6.4)
t
Q
!(
Q
-
2
m
)!
1
Usually, the value of p is ver y large in comparison to m , and using the Sterling's approxi-
mation for n !, the value of p is
2(
Qm
-+
0.5)
æ ö ÷
m
Q
ç
- ç ç ÷
1
÷
ç è ø
=- æ
p
1
(6.5)
(
Qm
-+
2 . )
ö ÷
2
m
Q
ç
÷
1
-
ç
÷
ç
÷
ç è
ø
Figure 6.1 shows the value of p for different values of Q and m . We observe that with
the increase in Q , there is a negligible increase in the key ring size m for the same value
of p . For example, for p = 0.5 and Q = 6000, the value of m = 68. Subsequently, if the
pool size is increased to 10,000, for the same value of p = 0.5, m is only increased to 95.
In this scheme, all nodes use the same key pool Q . This implies that the security of
the network is gradually eroded as keys from Q are compromised by an adversary that
captures more and more nodes. In this scheme, the number of exposed keys is roughly
Figure 6.1. Probability of Sharing At Leas
t One Shared Key Using Eschenauer and
Gligor's Scheme
Search WWH ::




Custom Search