Key Management - Everyday Cryptography - page 349

approximately 50%of themeasurements that he has just taken. This is because
there are two different types of polarisation detector that Bob can use to
measure each photon, and if he chooses the wrong one then the resulting
measurement has only a 50% chance of being correct. Alice advises him over
the authenticated channel which polarisation detector she used to encode
each qubit, and Bob throws away the returns of all the wrongly measured
photons.
4. Alice and Bob now conduct a check over the authenticated channel on the
stream of bits that they think they have just agreed upon. They do this by
randomly choosing some positions and then check to see if they both agree on
the bits in these positions. If they find no discrepancies then they throw away
the bits that were used to conduct the check, and form a key from the bits
that they have not yet checked.
To understand why this protocol works, consider the position of an attacker. This
attacker can take measurements of photons on the quantum channel and can
listen in to all the discussion on the authenticated channel. However, if the attacker
chooses to measure a photon on the quantum channel, and if the attacker uses the
wrong detector (which will happen in approximately 50% of the measurements)
then this process changes the polarisation, which in turn leads to Bob obtaining
an incorrect output bit. Thus such activity will be detected with high probability
by Alice and Bob when they do the 'spot check' of agreed bits. Alice and Bob can
set this probability to be as high as they like, simply by increasing the number of
bits that they check.
QUANTUM KEY ESTABLISHMENT IN PRACTICE
The theory behind quantum key establishment is certainly intriguing. However,
the motivation for quantum key establishment is all about overcoming practical
problems. Is quantum key establishment, itself, practical?
There are a number of substantial limitations of quantum key establishment.
These include:
Distance limitations . Implementations of quantum key establishment are
improving all the time. Nonetheless, it has still only been demonstrated to
work over limited distances. For example, in 1988 it was shown to work over
a 30 cm distance. This had improved by 2010 to around 150 km in an optical
fibre network, and several demonstration networks had been built that used
quantum key establishment. It is believed that a significant extension of the
underlying mechanisms will be required if distances over 400 km are ever to be
achieved in optical fibre networks. In contrast, there are no technical limits on
the distance over which most conventional key establishment techniques can
be used.
Data rates . There are limits to the rate at which key material can be exchanged
over the quantum channel. This is also related to the distance over which the
key establishment is being conducted.