07-02-2013, 04:39 PM
SEMINAR QUANTUM CRYPTOGRAPHY
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Abstract
Quantum cryptography could well be the rst application of quantum me-
chanics at the individual quanta level. In this paper I shall describe the theory
of quantum cryptography and how to perform quantum cryptography over an
optical ber communications link. This seminar reviews how quantum physics
allows information coding in classically unexpected ways. Quantum logic gates
and key distribution are also discussed.
Introduction
Human desire to communicate secretly is at least as old as writing itself and goes
back to the beginnings of our civilisation. Methods of secret communication were
developed by many ancient societies, including those of Mesopotamia, Egypt, India,
and China, but details regarding the origins of cryptology remain unknown.
Until some years ago, cryptography was restricted primarily to the military
world. Only the military had su¢ cient resources to produce mechanical devices,
such as the famous enigma which was widely used by Germans during World War
II or its American counterpart the M-209. Enigma ciphers were broken before at
Bletchley Park in England. The Bletchley Park team had to develop the electro-
mechanical tools to break these ciphers, which resulted in building the rst digital
computer called Colossus. Thus modern cryptology was born together with com-
puter science. [1]
Basic concepts in quantum computation
Consider the two binary strings: 011; 111: The rst one can represent, for example,
the number 3 (in binary) and the second one the number 7:
A qubit is a quantum system in which the Boolean states 0 and 1 are represented
by a prescribed pair of normalised and mutually orthogonal quantum states labeled
as fj0i; j1ig: The two states form a "computional basis" and any other state of the
qubit can be written as a superposition j0i + j1i for some and such that
jj2+jj2 = 1: A qubit is typically a microscopic system, such as an atom, a nuclear
spin, or a polarised photon. A collection of n qubits is called a quantum register of
size n:
Quantum key distribution
To understand QKD we must rst move away from the traditional key distribu-
tion, we should have in mind a more symmetrical starting point, in wich Alice and
Bob initially generate their own, independent random number sets, containing more
numbers than they need for key material that will ultimately share. Next, they
compare these sets of numbers to get a shared subset, which will become the key
material. Alice prepares a sequence of tokens, one kind of a "0" and a di¤rent 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 Alices 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). With Bobs information Alice and Bob can identify the
bits they have in common. They keep these bits, forming the key, and discard the
others. If one of Alices tokens fails to reach Bob this does not spoil the procedure,
because it is only tokens that arrive which are used in the process.
Practical implementations of QKD
For photons the quantum communication channel can either be free space or optical
bers-special bers or the ones used in standard telecommunication. The commu-
nication channel is thus not really quantum. What is quantum are the information
carriers. Perhaps the most obvious way to implement the QKD quantum channel is
with single-photon polarization states. Light is guided in optical bers thanks to the
refraction index pro le n(x; y) across the section of the bers. Over the last 25 years,
a lot of e¤ort has been made to reduce transmission losses- initially several dB per
km, and nowadays the attenuation is as low as 2 dB/km at 800 nm wavelength, 0.35
dB/km at 1320 nm, and 0.2 dB/km at 1550 nm (see Figure 7).