Cryptography Reference
In-Depth Information
where we have introduced the function
2
k
−
1
1
−
(
1
−
y
)
σ
e
(
k, y
)
=
.
(7.19)
1
−
2
1
−
k
σ
(
)
For a photon pulse with 2
k
photons,
is greater than 1 if the indirect
attack is stronger and less than 1 if the direct attack is stronger. For odd
numbers of photons, the direct attack is always stronger in this region [7].
The significance of these results for Eve is evident. If the key distribution
system is operating in the region of large
y
, her optimal attack is always the
indirect attack. If the system operates in the region of small
y
, the direct attack
is optimal. If the system operates in the middle region, Eve optimizes her
attack by measuring nondestructively the number of photons in the incoming
pulses and then selecting the attack for each pulse according to the number
of photons it contains.
In Figure 7.1 we plot the
y
-number line, divided into the three optimal
attack regions for multiphoton pulses subjected to any of the direct (USD),
indirect (PNS) or combined individual attacks. It should be noted that, for
many conceivable practical quantum cryptography systems, the values of
the relevant parameters are such that one will naturally be located in Region
II on the plot, which implies that
the direct (USD) attack is typically going to be
stronger than the indirect (PNS) attack.
For instance, a typical system may have
photon detectors with efficiencies of about
k, y
e
η
0
.
5, and the quantum channel
odd photon number: direct attack
even photon number:
1 - (1-
y
)
2
k
-1
1 - 2
1-
k
2k = number of photons
indirect attack
direct attack
σ
e
≡
σ
e
<
1
σ
e
>
1
direct attack
indirect attack
Region II
Region III
Region I
y
0
.206
.296
1
1
1
1
y
< 1
-
1 -
< y
< 1
-
1
-
< y
3
3
2
2
2
2
y
≡ ηα
: the value of
y
when the enemy
cannot
effectively eliminate the line attenuation
or
y
≡ η
: the value of
y
when the enemy
can
effectively eliminate the line attenuation
Figure 7.1
Optimal attack regions for multiphoton pulses.
