Both creating and breaking codes have become very important in our society, whether in computer programming, security, in life or death situations in wartime, and even in preventing wars during peace time. Cryptologists (that is, the people who study codes) are constantly searching for new methods for creating codes which might be more unbreakable than the last, and new ways to crack previous codes in order to prevent terrorist attacks or to know the positions and movements of certain enemies. It is something which is constantly happening in our world, even if we may be oblivious to it (in fact, sometimes it’s probably best that we remain oblivious to certain things – life’s just easier that way).
A Few Examples of Cryptography
Now in the past, a great deal of cryptography has been based on mathematics – messages may be encoded into numerical form, and the only way to crack the code is to have a certain key. Mathematicians have been hard at work for decades coming up with new and improved mathematical systems that, even if one were to use the most powerful computer, would take years to even begin to crack.
One of the crucial methods used in cryptography has been factorization. A code is sent in a series of very large numbers (numbers with hundreds or even thousands of digits) which need to be factored. The person (or computer) making the code has no problem – all they need to do is to multiply together two large prime numbers then send the resulting number to the recipient, who possesses some sort of key to being able to correctly find the appropriate factors (this is done with a large series of numbers).
It is obviously much more complicated than this in the real world, but this is the basic idea. Still, even though computers today are not powerful enough to be effective in cracking these codes, it is still very much possible, and therefore these codes cannot be considered “unbreakable.” Mathematicians have yet to discover the “perfect code”, which is absolutely unbreakable by those interested in such secret messages.
Quantum Cryptography
Physicists, on the other hand, may be on the right track.
There is a burgeoning field of theory out there known as quantum cryptography, which attempts to merge together the seemingly disparate worlds of quantum mechanics and cryptography together into a unified whole. The essence of the ideas behind this method of code-making lies in the theory which is at the heart of the quantum world – The Heisenberg Uncertainty principle.
In essence, Heisenberg’s principle states that there are only certain things about a quantum process which can possibly be known. In this is deeply embedded the idea of complementarily, which refers to the fact that in any quantum system there are certain measurements which depend directly on other measurements. For instance, if one was to attempt to measure the exact location of an electron, it would directly affect any attempted measurement of the electron’s velocity. As one becomes more sure of the electron’s location, one becomes less sure of its speed, and vice versa. These two measurements, in other words, are complimentary to each other.
Now, in quantum cryptography, this idea of complementarily is generally applied to particles of light (photons), which possess a quantum property called polarization, which can best be defined as the angle at which the light moves. Some light is polarized horizontally, some vertically, some at forty-five degree angles (and every angle in between). And it is this fact which enables us to possibly figure out how to send unbreakable codes.
In essence, it would go something like this:
Person one wants to send a message to Person two (in almost every explanation of these theories one finds that the two people are given the names Alice and Bob, credit for which is often given to a 1978 book on communications by Ron Rivest. Here, calling them simply Person one and Person two will do just fine), so he sends a series of photons through a medium (probably a fiber-optic cable) to person two – each photon polarized either vertically/horizontally or diagonally. Now, because of the uncertainty principle, person two cannot simply detect the original polarization of these photons – he must align his detector up at random in one of the pre-ordained directions of polarization. Because the polarization is inherently uncertain, when he does this, he has approximately a fifty-fifty chance of measuring the correct polarization. After this, person one and person two may communicate through even unsecure channels about the results in order to discover which photons were measured correctly, and which were measured incorrectly. The fifty percent or so that were measured wrong are then tossed aside, and what is left is a series of polarizations which may represent binary digits which now both person one and person two have in common, and which they can now use as a key for decoding a message.
But how does this method guarantee that the key couldn’t have been discovered by a third party, perhaps someone “eavesdropping” on the photon exchange? Simple. Again due to the uncertainty principle, if anyone had so much as attempted to measure a photon before it had arrived at person number two, the polarity of the photon would have changed due to complimentarily, which would mean that the code would no longer agree between person one and person two, and they would know there had been a breach in security and would have to try again.
Yes, it sounds a little complicated, but most of this would surely be automated in any true system of quantum cryptography. Though mathematicians certainly deserve credit for being undeniably intelligent and endlessly clever, the true frontier in cryptography rests squarely on the capable shoulders of quantum physicists. It is they who provide perhaps the best hope for ensuring that our important messages never fall into the wrong hands again.
References:
Gribbin, J. (1994). In Search of Schrodinger's Cat: Quantum Physics and Reality. New York, NY: Bantam Books.
Gribbin, J. (1995). Schrodinger's Kittens and the Search for Reality: Solving the Quantum Mysteries. New York, NY: Time Warner Book Group.
“Quantum Cryptography Tutorial.”
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