Quantum Cryptography


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Introduction

Cryptology, the mathematical science of secret communications, has a long
and distinguished history of military and diplomatic uses dating back to the
ancient Greeks.
2
In World War II, Allied successes in breaking the ciphers of
Germany and Japan played an important part in the outcome of the conflict and
the development of the modern computer.
3
Today, the ability to ensure the
secrecy of military or diplomatic communications is as vital as ever, but
cryptography is also becoming more and more important in everyday life.


Cryptography

To explain the significance of quantum cryptography it is necessary to
describe some of the important features (and perils) of cryptography in general.
These points can be illustrated with one of the most famous literary examples of a
cipher: Sir Arthur Conan Doyle’s “The Adventure of the Dancing Men.”
1
In this
story, Elsie, the American wife of an English gentleman, Hilton Cubbitt, is
terrorised by the appearance of chalked stick-figures outside her house. (See
Figure 1.) Sherlock Holmes is called in and quickly realises that the figures are not
the scribblings of children, but rather are a form of cryptography, in which each
letter of the alphabet has been substituted with a stick figure, known only to the
sender (Abe Slaney, “the most dangerous crook in Chicago”) and the intended
recipient, Elsie.



Quantum key distribution

To understand QKD we must first move away from the traditional key
distribution metaphor of Alice sending
particular
key data to Bob. Instead, we
should have in mind a more symmetrical starting point, in which Alice and Bob
initially generate their own, independent random number sets, containing more
numbers than they need for the key material that they will ultimately share. Next,
they compare these sets of numbers to distil a shared subset, which will become
the key material. It is important to appreciate that they do not need to identify
all
of their shared numbers, or even
particular
ones, because the only requirements
on the key material are that the numbers should be secret and random. They can
attempt to accomplish a secret distillation if Alice prepares a sequence of tokens,
one kind for a “0” and a different kind for a “1”, and sends a token to Bob for
each bit in her set. Bob proceeds through his set bit-by-bit in synchronisation with
Alice, and compares Alice’s token with his bit, and replies to Alice telling her
whether the token is the same as his number (but not the value of his bit).


Practical implementations of QKD
Perhaps the most obvious way to implement the QKD quantum channel is
with single-photon polarization states, such as the preparation of vertical and
right-handed-circular polarizations, and the measurement of horizontal linear and
left-handed-circular polarizations.