(scan to the end of this post for the answer to the question;
the first part is just background. The basic answer is that
QUANTUM ENCRYPTION provides a SECURE
WAY FOR TRASFERRING KEYS. After that, it's just standard traditional
encryption. Traditional encryption is NOT convenient. Public key methods
have made it more convenient, but they ALL can be broken with a finite
amount of computing time. Quantum encryption gets rid of the public
key methods and provides a true way to send a KEY without it ever being
sniffed. After the key is transferred, the same old traditional methods
are applied.)
Contents
Public Key Cryptography
Public key cryptography is a really amazing thing. You export a public
key that anyone else can use to encrypt data, but not decrypt it. You
then keep a private key that can decrypt that data. These two keys are
coupled together, so you really are exporting information about your
private key, but that information is extremely difficult to find. The
coupling involves primes. Prime factorization of very large numbers
is a difficult problem, so if large enough random primes are used, the
private key and public keys stay "decoupled." (unless someone has a few
hundred years to crunch the problem with conventional computing)
So public key cryptography ALWAYS can be cracked using a STANDARD SIMPLE
METHOD. However, conventional computing would take hundreds (or even
thousands) of years (ON AVERAGE) to actually run that method. Just keep
in mind that public key cryptography can CERTAINLY be cracked just as
long as enough computing power is tossed at it.
Simplifying the Prime Factorization Problem with Quantum Computing
Quantum computing provides a fascinating way of turning the prime
factorization problem into something more reasonable for conventional
computing. It doesn't make the process constant time or anything like
that, but it makes it manageable in polynomial time. It's able to do this
by operating on a quantum mechanical possibility wave function in such a
way that correlations between possible states are not broken (the wave
function doesn't "collapse") until the end of the operation. It's true
parallel processing without actually having to buy parallel processors.
[ I'd like to note that there is an area of research going on right now
that is investigating using the fabric of the cosmos for computing. The
next generation of particle accelerator (the one they're finishing at
CERN) will actually be able to create small black holes within the
collider. Information theorists are coming up with ideas on how to
actually dump matter into these black holes as "inputs" in such a way
that the resulting radiation that is emitted from the black hole is the
result of a computation. ]
So quantum computing provides a method for prime factorization that is
far more tractable on modern computers. This turns the public key
cryptography cracking problem into something that can be solved in a few
hours rather than a few hundred years. And this is what spells doom for
public key cryptography.
Traditional Encryption (A Superset of Quantum Encryption)
Before public key cryptography, parties had to agree on a key to share
between them. If I was communicating with 10 people, I would have 10 keys
(ciphers) for each of those 10 people, and each person would also have
a copy of her respective key.
Note that when I talk of "keys," I'm actually talking about an entire
method of encryption. A key is a procedure for encrypting and decrypting
information. There is no standard way of using a key to encrypt
information; the method IS the key. The method is the cipher. Because
of that, there is no standard way to break traditional encryption. You
basically have to throw a bunch of geniuses into a room and have them
stare at the encrypted codes until they find patterns. They are able to
guess the cipher. But this is an act of black magic. It's heuristic. There
are some guidelines, but there's no one way to do it.
So traditional encryption really faces no threat from quantum
computing. Quantum computing may allow for some quicker methods to chew
on data, but it won't break the method like public key cryptography. The
major problem with public key cryptography is that everyone already knows
the METHOD, they just have to figure out exactly which numbers to plug in.
The PROBLEM with traditional encryption is that you have to have a safe
way of getting the key to each of your partners. You might be able
to use public key encryption, for example, to encrypt your key. This
is actually how most software programs transmit cipher information
today anyway. However, if someone cracks your public key encryption,
then that person also can get your key and crack all of your other
communications. So in the end, the best way to give someone your key
is to personally HAND IT to them. Because of this problem, public
key cryptography is FAR MORE convenient. But that's a tradeoff. Real
encryption requires getting up and actually giving a physical key to
someone, but it means that the communication will always be safe. Public
key cryptography means sending the key along with the message, but with
enough computing power it can ALWAYS be broken (for CERTAIN).
[ Remember in Swordfish when Hugh Jackman's
character talks about encryption with a cipher that was destroyed on
implementation? He's talking about true encryption. He's talking about
writing software to encrypt and decrypt information and after compiling
it, destroying everything that was involved in its creation. All that
remains are tne encryption and decryption engines. ]
Quantum Encryption
Quantum encryption really isn't any special type of encryption. It's
just a way of transmitting your key. After that, it's just standard
encryption. But since quantum encryption gives us a CONVENIENT WAY
of SAFELY transmitting vital information about a key, then it makes
traditional encryption just as nice as public key cryptography
and FAR safer.
The Simple Explanation (without talking about photons)
With quantum encryption, two people, Abby and Bill, agree on a method
of encryption that requires some 1024bit key. All they need is a way to
get that key from Abby to Bill. Well, Abby has TWO WAYS of transmitting
a 1 or a 0 to Bill. Likewise, Bill has TWO WAYS to receive a 1 or a 0
from Abby. (so a 1 can be sent in two ways, and a 0 can be sent in two
ways; and likewise for reception) Abby generates 10,000 random bits. For
each bit she sends to Bill, she randomly decides which of the two ways
she can send it. Sometime she sends it method 1, and the other times
she sends it method 2. Likewise, Bill randomly decides which way he's
going to receive the bits. Sometimes he picks method 1 and sometimes he
picks method 2. More importantly, sometimes he picks the right method,
and sometimes he picks the wrong method. If he picks the wrong method,
he gets a random bit that has NO CORRELATION to the one that Abby sent. If
he picks the right method, he gets Abby's bit.
Now, after every one of the 10,000 bits was received, Abby and Bill call
each other on a PUBLIC CHANNEL. Bill then tells Abby which methods he used
to receive each bit, but HE DOES NOT advertise what bits he received. Abby
just tells him when he chose the right method. They agree that the first
1024 times Bill chose CORRECTLY will be the bits that they will use for
their key.
Now, let's say Eve has been listening in. Let's say that she is in between
Abby and Bill intercepting each bit as it gets transmitted. She also,
like Bill, can choose method 1 or method 2 to receive the bit. Every
time she intercepts a bit, she records what she found, and transmits
that result to Bill. Bill never even realizes that there has been a delay.
But what if Eve chooses wrong? Then the bit that she transmits to Bill
is a random bit that has NO CORRELATION to the one sent by Abby.
So let's go back to that phone call between Abby and Bill. Let's say they
find the first 1024+500=1524 spots that they agree on. Then let's say
Bill TELLS ABBY the first 500 of those bits. If those are the same bits
that Abby sent, then they simply toss them out and keep the remaining
1024 as their key. However, let's assume that Eve was listening in
during the transmission. ASSUMING that Eve wasn't lucky enough to pick
EVERY method EXACTLY right, then SOME of those first 500 bits will not
match the ones Abby sent. In this case, Eve's presence was detected
(and Eve's information is useless).
So that's all quantum encryption does. It gives an easy way to transmit
KEYS. Just like with public key cryptography, after the keys are
transmitted, traditional encryption can be used.
The More Detailed Explanation (with some photon talk)
The transmission of photons are often given as an example of the "methods"
that Abby and Bill used to send bits from Abby to Bill. Light can be
polarized horizontally, vertically, or some combination of the two. From
an electromagnetics perspective, this is the direction of the transverse
oscillation of the propogating wave. Picture a string. Pulling it left
or right and then releasing causes horizontal oscillations. Pulling it
up or down causes vertical oscillations. Pulling it up and down AND
left or right causes diagonal oscillations. Note that these diagonal
oscillations are actually the SUM of a horizontal oscillation and a
vertical oscillation. Likewise, you could model a horizontal oscillation
or a vertical oscillation as a sum of two diagonal oscillations.
When modeling a diagonal oscillation as two "rectilinear"
(horizontal and vertical) oscillations, the CORRELATIONS between the two
diagonal oscillations are EXTREMELY IMPORTANT. Imagine that one end of the
string is fixed and you are moving the other end. As you move your hand
to the right, if your hand also moves up, then you get positive sloping
motion. As you move your hand to the right, if your hand also mvoes down,
you get negative sloping motion. So if the VERTICAL MOTION is POSITIVELY
correlated with with horizontal motion, you get postively sloping diagonal
motion. Likewise, if the vertical motion is negatively correlated with
horizontal motion, you get negatively sloping diagonal motion.
[ Note that in real life, light isn't always linearly
polarized. Imagine that as you move your hand back and forth
horizontally, vertical motion reaches its MAXIMUM when your hand is in
the MIDDLE of its horizontal motion. As your hand reaches fullright, it
is in the MIDDLE of its vertical motion. In this case, we say that the
two directions are in quadrature, and the result is circular
polarization. Your hand, and thus the string, oscillates in a
circle. Note that circular modes CAN be setup in a string. Likewise,
circular modes of light can be setup in a medium. There may be aspects
of that medium that prevent that (like a string moving through a slot)
or aspects of the medium that only allow that (like a string moving in a
circular slot). This is beyond this discussion though. It's important to
note that we can setup filters that only allow the passage of light
polarized in a particular linear direction. With these filters we
can transmit light in any diagonal or rectilinear direction. ]
Now, Abby decides that a 1 is represented by vertical () or positive
sloping diagonal (/) light. She thus also decides that a 0 is horizontal
() or negative sloping diagonal (\) light. At each bit she transmits,
she just picks randomly one of her two options for how to transmit it.
Now, Bill (or EVE) has two filters he can use. One of them looks like an
X and only allows diagonal light to pass through it. The other looks like
a + and only allows rectilinear light to pass through it. Now, REMEMBER
that ALL DIAGONAL LIGHT is the SUM of two CORRELATED horizontal light
waves, and ALL HORIZONTAL LIGHT is the SUM of two CORRELATED vertical
light waves. (keep the string example in mind) If Abby sent a diagonal
light wave (/ or \) to Bill and he picks his rectilinear (+) filter,
SINCE **BOTH** RECTILINEAR DIRECTIONS have been allowed to pass through,
the DIAGONAL LIGHT will STILL appear on Bill's side.
NOW ENTER QUANTUM ELECTRODYNAMICS. LIGHT IS **NOT** A WAVE.
Abby did not send a wave through though. Abby sent a PHOTON that was
diagonally polarized. Photons have STATES. Abby's photon's "polarization
state" was set to "positively sloping diagonal (/)", for example. Now,
Bill's RECTILINEAR FILTER only allows photons of RECTILINEAR POLARIZATIONS
through. Bill is asking the photon "are you polarized horizontally or
vertically?" From a wave point of view, we would say that the wave is
actually a sum of two nearly identical horizontal and vertical waves. From
a QUANTUM point of view though, things are a little hairier. The photon
basically has to answer "50% of the photons passed through are horizontal,
and 50% of the photons passed through are vertical, and the correlations
between the two give the appearance of diagonal polarization." However,
photons can't talk. So the photon just plays his role, and if you pass
enough of them through, half of them will be horizontal and half of them
will be vertical.
And so because Bill chose incorrectly, he learns **NOTHING** from his
reading of Abby's transmission. HALF of the time his measurement is one
direction and HALF of the time it's another direction, and this is the
case REGARDLESS of Abby's choice. As long as Abby chooses diagonally
and Bill chooses rectilinearly, then Bill's measurement is NO BETTER
THAN A COIN TOSS. (this goes for Eve too)
So by asking for one photon rather than an entire wave, Bill "collapses"
the wave function. He loses all information about the correlations
between the two rectilinear components, and thus he loses all diagonal
information.
This is what is going on **BEHIND** the Heisenberg's Uncertainty Principle
(HUP). Bill CANNOT KNOW **BOTH** diagonal polarization and rectilinear
polarization. It's just an illformed question. Something cannot
be BOTH diagonally polarized AND rectilinearly polarized. Simiarly,
something cannot be both in ONE POSITION *AND* have ONE MOMENTUM. This
is the essense of the HUP. It's a property of WAVES. The HUP is simply a
CONSEQUENCE of the fact that EVERYTHING is a probabilistic wave function
underneath it all.
Conclusion (the answer to the question)
Quote from barbaricprogrammer
Quantum encryption is nearly perfect but it doesn't offer the
flexibility of the public key system, if i read it correctly you would
have to calibrate each optical receptor/transmitter too send the data,
but if not i believe you would also have to give them the key somehow
other than publicly announce part of your key?

Quantum encryption IS a transfer of keys. That's ALL it is. It
really should be called quantum key transfer or something like
that.
So quantum encryption MAKES traditional encryption MORE FLEXIBLE,
not less flexible. Traditional encryption CURRENTLY requires physical
contact. Quantum encryption gives us a SECURE COMMUNICATIONS
channel on which to send our KEYS **BEFORE** encryption.
See? Isn't that beautiful? Elegant? Really wonderful?
And now you can actually BUY packaged quantum channels that play the
role of Abby and Bill automatically. They are connected by means of
optical fiber. Right now the length of the fiber is restricted, but it's
getting longer. Eventually we might be able to do this over transAtlantic
fiber. Now, that'd be the day...
Quote from barbaricprogrammer
I've tried to read up on the subject but I've found various
different explanations of quantum encryption algorithms mostly dealing
with photonics.

I hope that explanation has given you the answer to your question while
also giving you an idea of what all the photonics pages were talking
about.
It's a complicated subject. It can take years just to get comfortable with
all the vocabularly. However, the IDEA is a simple one. The complicated
thing is actually figuring out how to implement the idea in nature.
