BACKGROUND AND PURPOSE

• Holy codes, batman! (by Skillz)
  • A post recommending Singh's The Code Book.
  
  
• Re: Holy codes, batman! (by barbaricprogrammer)
  • A post asking if quantum encryption is more inconvenient than conventional encryption.
  
  
• Quantum Computing, Conventional Encryption, and Quantum Encryption (by Theo)
  • The post reproduced below. It basically answers that quantum encryption makes safe traditional encryption more convenient as it provides a way to safely send cipher keys from one location to another.

(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.)

• Public Key Cryptography
  
  
• Simplifying the Prime Factorization Problem with Quantum Computing
  
  
• Traditional Encryption (A Superset of Quantum Encryption)
  
  
• Quantum Encryption
  • The Simple Explanation (without talking about photons)
  • The More Detailed Explanation (with some photon talk)
  
  
• Conclusion (the answer to the question)

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.

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.

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 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)

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 full-right, 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 ill-formed 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.

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?

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.