 - Quantum cryptography uses our current knowledge of
physics to develop a cryptosystem that is not able to be
defeated - that is, one that is completely secure against being compromised
without knowledge of the sender or the receiver of the messages. The word quantum itself refers to the most fundamental behavior of the smallest particles of matter and energy: quantum theory explains everything that exists and nothing can be in violation of it.
Quantum cryptography is different from traditional cryptographic systems
in that it relies more on physics, rather than mathematics, as a key aspect of its security model.
Essentially, quantum cryptography is based on the usage of individual
particles/waves of light (photon) and their intrinsic quantum properties to develop an unbreakable cryptosystem - essentially because
it is impossible to measure the quantum state of any system without
disturbing that system. It is theoretically possible that other
particles could be used, but photons offer all the necessary qualities
needed, their behavior is comparatively well-understood, and they are
the information carriers in optical fiber cables, the most promising
medium for extremely high-bandwidth communications.
How It Works in Theory
In theory, quantum cryptography works in the following manner (this view is the "classical" model developed by Bennett and
Brassard in 1984 - some other models do exist):
Assume that two people wish to exchange a message securely,
traditionally named Alice and Bob. Alice initiates the message by sending Bob
a key, which will be the mode for encrypting the message data. This is a
random sequence of bits, sent using a certain type of scheme, which can
see two different initial values represent one particular binary value
(0 or 1).
Let us assume that this key is a stream of photons travelling in one
direction, with each of these photon particles representing a single bit
of data (either a 0 or 1). However, in addition to their linear travel,
all of these photons are oscillating (vibrating) in a certain manner.
These oscillations can occur in any 360-degree range across any
conceivable axis, but for the purpose of simplicity (at least as far as
it is possible to simplify things in quantum cryptography), let us
assume that their oscillations can be grouped into 4 particular states:
we'll define these as UP/DOWN, LEFT/RIGHT, UPLEFT/RIGHTDOWN and
UPRIGHT/LEFTDOWN. The angle of this vibration is known as the
polarization of the photon. Now, let us introduce a polarizer into the
equation. A polarizer is simply a filter that permits certain photons to
pass through it with the same oscillation as before and lets others pass
through in a changed state of oscillation (it can also block some
photons completely, but let's ignore that property for this exercise).
Alice has a polarizer that can transmit the photons in any one of the
four states mentioned - in effect, she can choose either rectilinear
(UP/DOWN and LEFT/RIGHT) or diagonal (UPLEFT/RIGHTDOWN and
UPRIGHT/LEFTDOWN) polarization filters.
Alice swaps her polarization scheme between rectilinear and diagonal
filters for the transmission of each single photon bit in a random
manner. In doing so, the transmission can have one of two polarizations
represent a single bit, either 1 or 0, in either scheme she uses.
When receiving the photon key, Bob must choose to measure each photon
bit using either his rectilinear or diagonal polarizer: sometimes he
will choose the correct polarizer and at other times he will choose the
wrong one. Like Alice, he selects each polarizer in a random manner. So
what happens with the photons when the wrong polarizer is chosen?
The Heisenberg Uncertainty Principle states that we do not know exactly
what will happen to each individual photon, for in the act of measuring
its behavior, we alter its properties (in addition to the fact that if
there are two properties of a system that we wish to measure, measuring
one precludes us from quantifying the other). However, we can make a
guess as to what happens with them as a group. Suppose Bob uses a
rectilinear polarizer to measure UPLEFT/RIGHTDOWN and UPRIGHT/LEFTDOWN
(diagonal) photons. If he does this, then the photons will pass through
in a changed state - that is, half will be transformed to UP/DOWN and the
other half to LEFT/RIGHT. But we cannot know which individual photons
will be transformed into which state (it is also a reality that some
photons may be blocked from passing altogether in a real world
application, but this is not relevant to the theory).
Bob measures some photons correctly and others incorrectly. At this
point, Alice and Bob establish a channel of communication that can be
insecure - that is, other people can listen in. Alice then proceeds to
advise Bob as to which polarizer she used to send each photon bit - but
not how she polarized each photon. So she could say that photon number
8597 (theoretically) was sent using the rectilinear scheme, but she will
not say whether she sent an UP/DOWN or LEFT/RIGHT. Bob then confirms if
he used the correct polarizer to receive each particular photon. Alice
and Bob then discard all the photon measurements that he used the wrong
polarizer to check. What they have, is, on average, a sequence of 0s and
1s that is half the length of the original transmission...but it will
form the basis for a one-time pad, the only cryptosystem that, if properly implemented, is proven to be completely random and secure.
Now, suppose we have an eavesdropper, Eve, who attempts to listen in,
has the same polarizers that Bob does and must also randomly choose
whether to use the rectilinear or diagonal one for each photon. However,
she also faces the same problem that Bob does, in that half the time she
will choose the wrong polarizer. But Bob has the advantage of speaking
to Alice to confirm which polarizer type was used for each photon. This
is useless to Eve, as half the time she used the wrong detector and will
misinterpret some of the photons that will form that final key,
rendering it useless.
Furthermore, there is another level of security inherent in quantum
cryptography - that of intrusion detection. Alice and Bob would know if
Eve was eavesdropping on them. The fact that Eve is on the "photon
highway" can become obvious because of the following.
Let's say that Alice transmits photon number 349 as an UPRIGHT/LEFTDOWN
to Bob, but for that one, Eve uses the rectilinear polarizer, which can
only measure UP/DOWN or LEFT/RIGHT photons accurately. What Eve will do
is transform that photon into either UP/DOWN or LEFT/RIGHT, as that is
the only way the photon can pass. If Bob uses his rectilinear polarizer,
then it will not matter what he measures as the polarizer check Alice
and Bob go through above will discard that photon from the final key.
But if he uses the diagonal polarizer, a problem arises when he measures
its polarization; he may measure it correctly as UPRIGHT/LEFTDOWN, but
he stands an equal chance, according to the Heisenberg Uncertainty
Principle, of measuring it incorrectly as UPLEFT/RIGHTDOWN. Eve's use of
the wrong polarizer will warp that photon and will cause Bob to make
errors even when he is using the correct polarizer.
To discover Eve's nefarious doings, they must perform the above
procedures, with which they will arrive at an identical key sequence of
0s and 1s - unless someone has been eavesdropping, whereupon there will
be some discrepancies. They must then undertake further measures to
check the validity of their key. It would be foolish to compare all the
binary digits of the final key over the unsecured channel discussed
above, and also unnecessary.
Let us assume that the final key comprises 4,000 binary digits. What
needs to be done is that a subset of these digits be selected randomly
by Alice and Bob, say 200 digits, in terms of both position (that is, digit
sequence number 2, 34, 65, 911 etc) and digit state (0 or 1). Alice and
Bob compare these - if they match, then there is virtually no chance
that Eve was listening. However, if she was listening in, then her
chances of being undiscovered are one in countless trillions, that is, no
chance in the real world. Alice and Bob would know someone was listening
in and then would not use the key - they would need to start the key
exchange again over a secure channel inaccessible to Eve, even though
the comparisons between Alice and Bob discussed above can still be done
over an insecure channel. However, even if Alice and Bob have concluded
that the their key is secure, since they have communicated 200 digits
over an un-secure channel, these 200 digits should be discarded from the
final key, turning it from a 4,000 into a 3,800 bit key).
Thus, quantum cryptography is a way to combine the relative ease and
convenience of key exchange in public key cryptography with the ultimate
security of a onetime pad.
How It Works in Practice
In practice, quantum cryptography has been demonstrated in the laboratory by IBM and others, but over
relatively short distances. Recently, over longer distances, fiber optic
cables with incredibly pure optic properties have successfully
transmitted photon bits up to 60 kilometers. Beyond that, BERs (bit error rates) caused by a combination of the Heisenberg Uncertainty Principle and microscopic impurities in the fiber make the system
unworkable. Some research has seen successful transmission through the
air, but this has been over short distances in ideal weather conditions.
It remains to be seen how much further technology can push forward the
distances at which quantum cryptography is practical.
Practical applications in the US are suspected to include a dedicated
line between the White House and Pentagon in Washington, and some links
between key military sites and major defense contractors and research
laboratories in close proximity.
| CONTRIBUTORS: |
and assistance provided by Borys Pawliw |
| LAST UPDATED: |
20 Jul 2004
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