Cryptography Reference
In-Depth Information
The major difference between the 4
+
2 state protocol and our cryptography
scheme is in the receiver: the 4
2 state scheme relies on photon counting,
whereas our system makes use of homodyne detection.
The key distribution protocol presented works with a BB84-type prepare
and measure strategy. By small modulations of the
S
1
polarized cw beam, four
coherent states with slightly positive (negative)
S
2
and
S
3
are produced with
the overlap chosen small enough to render these states nonorthogonal (cf.
Figure 5.3). Alice randomly prepares one of these four states and sends it to
Bob. Bob chooses randomly a measurement basis out of
S
2
and
S
3
. Figure 5.4
shows possible measurement outcomes for Bob, when he uses a 50 : 50 beam
splitter to measure
S
2
on one half and
S
3
on the other half of the beam (see also
Figure 5.12). By assigning a bit value 1 (0) to a positive (negative) measurement
result in both
S
2
and
S
3
bases, a shared key can be established.
The important constituent of the continuous variable system that forms
a distinct difference from conventional single-photon BB84 and 4
+
2 state
protocols is the postselection. It should be intentionally incorporated in the
protocol, whereas for single photons it is granted for free by nature: the pho-
tons affected by the loss do not arrive at the receiver. They are postselected
[20]. In contrast to original BB84, Bob has to choose a postselection thresh-
old
x
0
according to the actual key distribution data (Figure 5.1). The optimal
threshold is determined by the overlap
f
and attained information advantage
I
AB
+
−
I
AE
, which means by the amplitude
|
α
|
and observed channel transmi-
tivity
(loss level).
Bob discards all his measurement results that did not exceed the post-
selection threshold. For the remaining measurement results with low
p
e
,he
announces his measurement bases and corresponding time slots through the
public channel, so that Alice knows Bob's measurement results with high
probability. In the case of vanishing overlap between the states, this proce-
dure is deterministic and hence insecure. An eavesdropper may discriminate
between all four states and launch an intercept-resend attack without being
noticed. By using states with a considerable overlap, the error probability for
Eve increases, while Bob and Alice can postselect favorable events.
It is interesting to establish connections among and within the discrete
cryptographic systems and their continuous counterparts and to point out
the differences. The tight relation between the four-state BB84 protocol, the
two-state B92, and the 4
η
2 state protocol was already discussed in the be-
ginning of this section. We would like to suggest here a few more analogies.
The coherent state continuous variable scheme of Grangier and coworkers
[18,22] can be interpreted as the BB84 protocol with many bases and ho-
modyne detection which uses reverse reconciliation to render the secret key
generation possible also at high loss level. The scheme of Hirano and Namiki
with coworkers [19,24] is similar to the BB84 protocol with two bases but uses
homodyne detection and postselection as a reconciliation procedure to sup-
port the security. The continuous variable systems [18,19,22,24] encode the
signals in quadrature amplitudes. The discrete variable systems use mostly
polarization or phase encoding [2]. All these schemes operate at very low light
+
