Cryptography Reference
In-Depth Information
of leakage given by Shannon entropy [9]:
h
(
e
T
/
n
)
q
min
=
nh
(
e
T
/
n
)
=
e
T
(7.9)
e
T
/
n
The next term,
t
, is an upper bound for the amount of information Eve can
obtain by direct measurement of the polarizations of single-photon pulses.
This upper bound can be expressed as
t
=
Te
T
(7.10)
where
T
is given by [7,10,11]
n
1
e
T
−
I
max
e
T,
1
e
T,
1
e
T
T
(
n
1
,e
T
,e
T,
1
,
)
=
n
1
+
ξ(
n
1
,
)
1
1
/
2
n
1
e
T
e
T,
1
n
1
+
ξ(
n
1
,
)
−
,
(7.11)
with
1
2
,
1
1
2
−
3
ζ
I
max
(ζ )
≡
1
+
log
2
−
(7.12)
1
−
ζ
and
ξ
is defined by
1
√
2
n
1
erf
−
1
ξ(
n
1
,
)
≡
(
1
−
).
(7.13)
is a security parameter that gives the likelihood for
a successful eavesdropping attack against a single-photon pulse in the stream.
Finally, we have used
In the above equation
r
d
m
2
=
ψ
(ηµα)(
−
)
+
n
1
1
r
d
(7.14)
1
and
r
c
ψ
1
(ηµα)(
,
m
2
r
d
2
e
T,
1
=
1
−
r
d
)
+
(7.15)
which are the contributions to
n
and
e
T
from the subset of Alice's pulses for
which exactly one photon reaches Bob.
The next term,
, is the information leaked to Eve by making attacks on
pulses containing more than one photon. There are a variety of possible at-
tacks, including coherent attacks that operate collectively on all the photons
in the pulse. We restrict our attention to disjoint attacks that single out each
individual photon. Even with this restriction, there are a number of alterna-
tives. It is not clear that all possible attacks with this restriction have been
enumerated in research carried out to date. In this analysis, we consider the
situation in which Eve can carry out three important types of attacks. Eve can
perform a
direct
attack by making direct measurements of the polarization
of some subset of the photons and allowing the rest to continue undisturbed
(this is sometimes called an “unambiguous state discrimination” (USD) at-
tack). She can also perform an
indirect
attack by storing some of the photons
ν
