Cryptography Reference
In-Depth Information
Assume that user j wants to broadcast a message m . It first obtains its private key
as d j = H 1 ( ID j || t i ), where ID j is the ID of node j , and t i is the time-stamp of the time
interval in the current round from TDMA (time division multiple access) control.
The sensor then picks a random
*
q
α
Î and computes = e ( P,P ) . The sensor node
Z
further computes
c j = H 2 ( m || t i || )
(7.4)
and let
j = c j d j + P
(7.5)
σ
,
c
is the digital signature on the message m . The broadcast message is now
concatenated in the form of
where
j
j
σ
ID
,, , ,
t
m
c
(7.6)
j
i
j
j
σ
Upon receiving
each sensor node verifies the authenticity in the fol-
lowing way: It checks the time-stamp of the current time interval t i and determines
whether the received message is fresh. Then, if the time-stamp is correct, the sensor
node further computes
ID
,, , ,
t
m
c
,
j
i
j
j
c
¢ =
θ σ
e
(,
Pe HIDt
)((
||
,
-
P
) j
(7.7)
j
1
j
i
pub
¢
Using the time-stamp of the current time interval t i and a random for deriving
θ
,
¢ to . We should
θ
the sensor node does the bilinear transformation and mapping from
have the formula below, if the received message is authentic:
c
¢ =
θ σ
-
e
(,
Pe HIDt
)((
||
,
P
)
j
j
1
j
i
pub
c
=
σ
-
τ
e
(,
Pe HIDt
)((
||
,
P
)
j
j
1
j
i
c
=+
ecd
(
α
PP eH ID
,
) (
(
||
t
),
-
τ
P
)
j
j
j
1
j
i
c
=+
α
τ
ecd
(
PP e H ID
,
) (
(
||
t
),
P
)
j
j
j
1
j
i
-
c
α
c
=
τ
(( , ) ( , ) )(
ed P
j
ePP
e H ID
(
|| ), )
t
P
j
j
1
j
i
c
-
c
α
=
=
ed P
(,)(,)(,)
(, )
j
ePP ed P
j
j
j
α
ePP
=
θ
(7.8)
¢ = = which is equal to that in the received mes-
sage, the sensor node considers the received message authentic and transmits the mes-
sage to the next hop or user. If the verification above fails, the sensor node considers the
message as a bogus or replaced one, even a mistaken one, and ignores it.
The sensor nodes that decide to become cluster heads broadcast an advertisement
message ( adv ) along with their digital signature to all sensor nodes in the network.
θ
θ
Then, if
hm t
( | | )
hm t
( | |)
c
,
i
i
j
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