Quantum Cryptography
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22-09-2008, 09:56 AM


Definition
Quantum cryptography is an effort to allow two users of a common communication channel to create a body of shared and secret information. This information, which generally takes the form of a random string of bits, can then be used as a conventional secret key for secure communication. It is useful to assume that the communicating parties initially share a small amount of secret information, which is used up and then renewed in the exchange process, but even without this assumption exchanges are possible.

The advantage of quantum cryptography over traditional key exchange methods is that the exchange of information can be shown to be secure in a very strong sense, without making assumptions about the intractability of certain mathematical problems. Even when assuming hypothetical eavesdroppers with unlimited computing power, the laws of physics guarantee (probabilistically) that the secret key exchange will be secure, given a few other assumptions.
Cryptography is the art of devising codes and ciphers, and cryptoanalysis is the art of breaking them. Cryptology is the combination of the two. In the literature of cryptology, information to be encrypted is known as plaintext, and the parameters of the encryption function that transforms are collectively called a key.

Existing cryptographic techniques are usually identified as ``traditional'' or ``modern.'' Traditional techniques date back for centuries, and are tied to the the operations of transposition (reordering of plaintext) and substitution (alteration of plaintext characters). Traditional techniques were designed to be simple, and if they were to be used with great secrecy extremely long keys would be needed. By contrast, modern techniques rely on convoluted algorithms or intractable problems to achieve assurances of security.

There are two branches of modern cryptographic techniques: public-key encryption and secret-key
encryption. In public-key cryptography, messages are exchanged using keys that depend on the assumed difficulty of certain mathematical problems -- typically the factoring of extremely large (100+ digits) prime numbers. Each participant has a ``public key'' and a ``private key''; the former is used by others to encrypt messages, and the latter by the participant to decrypt them.

In secret-key encryption, a k-bit ``secret key'' is shared by two users, who use it to transform plaintext inputs to an encoded cipher. By carefully designing transformation algorithms, each bit of output can be made to depend on every bit of the input. With such an arrangement, a key of 128 bits used for encoding results in a key space of two to the 128th (or about ten to the 38th power). Assuming that brute force, along with some parallelism, is employed, the encrypted message should be safe: a billion computers doing a billion operations per second would require a trillion years to decrypt it. In practice, analysis of the encryption algorithm might make it more vulnerable, but increases in the size of the key can be used to offset this.

The main practical problem with secret-key encryption is determining a secret key. In theory any two users who wished to communicate could agree on a key in advance, but in practice for many users this would require secure storage and organization of a awkwardly large database of agreed-on keys.
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14-02-2009, 11:33 PM

The idea that a vote cast by a person remains the same after he submitted it is taken very seriously in any democracy. Voting is the right of the citizen, and it's how we choose the people who make important decisions on our behalf. When the security of the ballot is compromised, so, too, is the individual's right to choose his leaders.

Quantum Suicide Image Gallery
Voters waiting to cast their votes in Switizerland via quantum cryptogoraphy
Fabrice Coffrini/AFP/Getty Images
Votes cast in the Swiss canton of Geneva were protected for the first time by quantum cryptography. See quantum suicide images.
There are plentiful examples of vote tampering throughout history in the United States and in other countries. Votes get lost, the dead manage to show up on the poll results, and sometimes votes are even changed when they're tallied.

But, hopefully, the days when paper ballots get lost on the back roads of Florida en route to be counted will soon be gone, and the hanging chad will become an obscure joke on sitcom reruns from the early 21st century. In other words, it's possible that the votes we cast will soon become much more secure.

One of the ways to safeguard votes is to limit access to them when they're being transferred from precincts to central polling stations where they're tallied. And this is just what the Swiss are looking into. The nation best known for its neutrality is on the cutting edge of research into quantum cryptography. But unlike traditional cryptology methods -- encoding and decoding information or messages -- quantum cryptology depends on physics, not mathematics.
U­sing a machine developed by Swiss manufacturer Id Quantique, votes cast in the Swiss canton of Geneva during the October 2007 parliamentary elections were transmitted using a secure encryption encoded by a key generated using photons -- tiny, massless packets of light. Since this method uses physics instead of math to create the key used to encrypt the data, there's little chance it can be cracked using mathematics. In other words, the votes cast by citizens in Geneva are more protected than ever.

Id Quantiques' quantum encryption is the first public use of such a technique. What's more, it has catapulted the little-known world of quantum cryptology onto the world stage. So how does it work? Since it's based on quantum physics -- the smallest level of matter science has been able to detect -- it can seem a little confusing. But don't worry, even quantum physicists find quantum physics incredibly perplexing.

In this article, we'll get to the bottom of how quantum encryption works, and how it differs from modern cryptology. But first, we'll look at the uses and the limitations of traditional cryptology methods.
Traditional Cryptology
A German Enigma machine
Photo courtesy NSA
A German Enigma machine
Privacy is paramount when communicating sensitive information, and humans have invented some unusual ways to encode their conversations. In World War II, for example, the Nazis created a bulky machine called the Enigma that resembles a typewriter on steroids. This machine created one of the most difficult ciphers (encoded messages) of the pre-computer age.

Even after Polish resistance fighters made knockoffs of the machines -- complete with instructions on how the Enigma worked -- decoding messages was still a constant struggle for the Allies [source: Cambridge University]. As the codes were deciphered, however, the secrets yielded by the Enigma machine were so helpful that many historians have credited the code breaking as a important factor in the Allies' victory in the war.

What the Enigma machine was used for is called cryptology. This is the process of encoding (cryptography) and decoding (cryptoanalysis) information or messages (called plaintext). All of these processes combined are cryptology. Until the 1990s, cryptology was based on algorithms -- a mathematical process or procedure. These algorithms are used in conjunction with a key, a collection of bits (usually numbers). Without the proper key, it's virtually impossible to decipher an encoded message, even if you know what algorithm to use.

There are limitless possibilities for keys used in cryptology. But there are only two widely used methods of employing keys: public-key cryptology and secret-key cryptology. In both of these methods (and in all cryptology), the sender (point A) is referred to as Alice. Point B is known as Bob.

In the public-key cryptology (PKC) method, a user chooses two interrelated keys. He lets anyone who wants to send him a message know how to encode it using one key. He makes this key public. The other key he keeps to himself. In this manner, anyone can send the user an encoded message, but only the recipient of the encoded message knows how to decode it. Even the person sending the message doesn't know what code the user employs to decode it.

PKC is often compared to a mailbox that uses two keys. One unlocks the front of the mailbox, allowing anyone with a key to deposit mail. But only the recipient holds the key that unlocks the back of the mailbox, allowing only him to retrieve the messages.

The other usual method of traditional cryptology is secret-key cryptology (SKC). In this method, only one key is used by both Bob and Alice. The same key is used to both encode and decode the plaintext. Even the algorithm used in the encoding and decoding process can be announced over an unsecured channel. The code will remain uncracked as long as the key used remains secret.

SKC is similar to feeding a message into a special mailbox that grinds it together with the key. Anyone can reach inside and grab the cipher, but without the key, he won't be able to decipher it. The same key used to encode the message is also the only one that can decode it, separating the key from the message.

Traditional cryptology is certainly clever, but as with all encoding methods in code-breaking history, it's being phased out. Find out why on the next page.
Traditional Cryptology Problems
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Both the secret-key and public-key methods of cryptology have unique flaws. Oddly enough, quantum physics can be used to either solve or expand these flaws.
Code
Henkster/SXC

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The keys used to encode messages are so long that it would take a trillion years to crack one using conventional computers.
The problem with public-key cryptology is that it's based on the staggering size of the numbers created by the combination of the key and the algorithm used to encode the message. These numbers can reach unbelievable proportions. What's more, they can be made so that in order to understand each bit of output data, you have to also understand every other bit as well. This means that to crack a 128-bit key, the possible numbers used can reach upward to the 1038 power [source: Dartmouth College]. That's a lot of possible numbers for the correct combination to the key.

The keys used in modern cryptography are so large, in fact, that a billion computers working in conjunction with each processing a billion calculations per second would still take a trillion years to definitively crack a key [source: Dartmouth College]. This isn't a problem now, but it soon will be. Current computers will be replaced in the near future with quantum computers, which exploit the properties of physics on the immensely small quantum scale. Since they can operate on the quantum level, these computers are expected to be able to perform calculations and operate at speeds no computer in use now could possibly achieve. So the codes that would take a trillion years to break with conventional computers could possibly be cracked in much less time with quantum computers. This means that secret-key cryptology (SKC) looks to be the preferred method of transferring ciphers in the future.

But SKC has its problems as well. The chief problem with SKC is how the two users agree on what secret key to use. If you live next door to the person with whom you exchange secret information, this isn't a problem. All you have to do is meet in person and agree on a key. But what if you live in another country? Sure, you could still meet, but if your key was ever compromised, then you would have to meet again and again.

It's possible to send a message concerning which key a user would like to use, but shouldn't that message be encoded, too? And how do the users agree on what secret key to use to encode the message about what secret key to use for the original message? The problem with secret-key cryptology is that there's almost always a place for an unwanted third party to listen in and gain information the users don't want that person to have. This is known in cryptology as the key distribution problem.

It's one of the great challenges of cryptology: To keep unwanted parties -- or eavesdroppers -- from learning of sensitive information. After all, if it was OK for just anyone to hear, there would be no need to encrypt a message.

Quantum physics has provided a way around this problem. By harnessing the unpredictable nature of matter at the quantum level, physicists have figured out a way to exchange information on secret keys. Coming up, we'll find out how quantum physics has revolutionized cryptology. But first, a bit on photons.
Photon Properties

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Photons are some pretty amazing particles. They have no mass, they're the smallest measure of light, and they can exist in all of their possible states at once, called the wave function. This means that whatever direction a photon can spin in -- say, diagonally, vertically and horizontally -- it does all at once. Light in this state is called unpolarized. This is exactly the same as if you constantly moved east, west, north, south, and up-and-down at the same time. Mind-boggling? You bet. But don't let this throw you off; even quantum physicists are grappling with the implications of the wave function.
Photon polorization process
The foundation of quantum physics is the unpredictability factor. This unpredictability is pretty much defined by Heisenberg's Uncertainty Principle. This principle says, essentially, that it's impossible to know both an object's position and velocity -- at the same time.

But when dealing with photons for encryption, Heisenberg's principle can be used to our advantage. To create a photon, quantum cryptographers use LEDs -- light emitting diodes, a source of unpolarized light. LEDs are capable of creating just one photon at a time, which is how a string of photons can be created, rather than a wild burst. Through the use of polarization filters, we can force the photon to take one state or another -- or polarize it. If we use a vertical polarizing filter situated beyond a LED, we can polarize the photons that emerge: The photons that aren't absorbed will emerge on the other side with a vertical spin ( | ).

The thing about photons is that once they're polarized, they can't be accurately measured again, except by a filter like the one that initially produced their current spin. So if a photon with a vertical spin is measured through a diagonal filter, either the photon won't pass through the filter or the filter will affect the photon's behavior, causing it to take a diagonal spin. In this sense, the information on the photon's original polarization is lost, and so, too, is any information attached to the photon's spin.

So how do you attach information to a photon's spin? That's the essence of quantum cryptography. Read the next page to find out how quantum cryptography works.
Using Quantum Cryptology

Quantum cryptography uses photons to transmit a key. Once the key is transmitted, coding and encoding using the normal secret-key method can take place. But how does a photon become a key? How do you attach information to a photon's spin?
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How photons become keys
This is where binary code comes into play. Each type of a photon's spin represents one piece of information -- usually a 1 or a 0, for binary code. This code uses strings of 1s and 0s to create a coherent message. For example, 11100100110 could correspond with h-e-l-l-o. So a binary code can be assigned to each photon -- for example, a photon that has a vertical spin ( | ) can be assigned a 1. Alice can send her photons through randomly chosen filters and record the polarization of each photon. She will then know what photon polarizations Bob should receive.

When Alice sends Bob her photons using an LED, she'll randomly polarize them through either the X or the + filters, so that each polarized photon has one of four possible states: (|), (--), (/) or ( ) [source: Vittorio]. As Bob receives these photons, he decides whether to measure each with either his + or X filter -- he can't use both filters together. Keep in mind, Bob has no idea what filter to use for each photon, he's guessing for each one. After the entire transmission, Bob and Alice have a non-encrypted discussion about the transmission.

The reason this conversation can be public is because of the way it's carried out. Bob calls Alice and tells her which filter he used for each photon, and she tells him whether it was the correct or incorrect filter to use. Their conversation may sound a little like this:

* Bob: Plus
Alice: Correct
* Bob: Plus
Alice: Incorrect
* Bob: X
Alice: Correct

Since Bob isn't saying what his measurements are -- only the type of filter he used -- a third party listening in on their conversation can't determine what the actual photon sequence is.

Here's an example. Say Alice sent one photon as a ( / ) and Bob says he used a + filter to measure it. Alice will say "incorrect" to Bob. But if Bob says he used an X filter to measure that particular photon, Alice will say "correct." A person listening will only know that that particular photon could be either a ( / ) or a ( ), but not which one definitively. Bob will know that his measurements are correct, because a (--) photon traveling through a + filter will remain polarized as a (--) photon after it passes through the filter.

After their odd conversation, Alice and Bob both throw out the results from Bob's incorrect guesses. This leaves Alice and Bob with identical strings of polarized protons. It my look a little like this: -- / | | | / -- -- | | | -- / | ¦ and so on. To Alice and Bob, this is a meaningless string of photons. But once binary code is applied, the photons become a message. Bob and Alice can agree on binary assignments, say 1 for photons polarized as ( ) and ( -- ) and 0 for photons polarized like ( / ) and ( | ).

This means that their string of photons now looks like this: 11110000011110001010. Which can in turn be translated into English, Spanish, Navajo, prime numbers or anything else the Bob and Alice use as codes for the keys used in their encryption.
Introducing Eve
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The goal of quantum cryptology is to thwart attempts by a third party to eavesdrop on the encrypted message. In cryptology, an eavesdropper is referred to as Eve.
Detecting an eavesdropper, E for Eve, during photon transmission between points A, Alice, and B, Bob.
In modern cryptology, Eve (E) can passively intercept Alice and Bob's encrypted message -- she can get her hands on the encrypted message and work to decode it without Bob and Alice knowing she has their message. Eve can accomplish this in different ways, such as wiretapping Bob or Alice's phone or reading their secure e-mails.

Quantum cryptology is the first cryptology that safeguards against passive interception. Since we can't measure a photon without affecting its behavior, Heisenberg's Uncertainty Principle emerges when Eve makes her own eavesdrop measurements.

Here's an example. If Alice sends Bob a series of polarized photons, and Eve has set up a filter of her own to intercept the photons, Eve is in the same boat as Bob: Neither has any idea what the polarizations of the photons Alice sent are. Like Bob, Eve can only guess which filter orientation (for example an X filter or a + filter) she should use to measure the photons.

After Eve has measured the photons by randomly selecting filters to determine their spin, she will pass them down the line to Bob using her own LED with a filter set to the alignment she chose to measure the original photon. She does to cover up her presence and the fact that she intercepted the photon message. But due to the Heisenberg Uncertainty Principle, Eve's presence will be detected. By measuring the photons, Eve inevitably altered some of them.

Say Alice sent to Bob one photon polarized to a ( -- ) spin, and Eve intercepts the photon. But Eve has incorrectly chosen to use an X filter to measure the photon. If Bob randomly (and correctly) chooses to use a + filter to measure the original photon, he will find it's polarized in either a ( / ) or ( ) position. Bob will believe he chose incorrectly until he has his conversation with Alice about the filter choice.

After all of the photons are received by Bob, and he and Alice have their conversation about the filters used to determine the polarizations, discrepancies will emerge if Eve has intercepted the message. In the example of the ( -- ) photon that Alice sent, Bob will tell her that he used a + filter. Alice will tell him this is correct, but Bob will know that the photon he received didn't measure as ( -- ) or ( | ). Due to this discrepancy, Bob and Alice will know that their photon has been measured by a third party, who inadvertently altered it.

Alice and Bob can further protect their transmission by discussing some of the exact correct results after they've discarded the incorrect measurements. This is called a parity check. If the chosen examples of Bob's measurements are all correct -- meaning the pairs of Alice's transmitted photons and Bob's received photons all match up -- then their message is secure.

Bob and Alice can then discard these discussed measurements and use the remaining secret measurements as their key. If discrepancies are found, they should occur in 50 percent of the parity checks. Since Eve will have altered about 25 percent of the photons through her measurements, Bob and Alice can reduce the likelihood that Eve has the remaining correct information down to a one-in-a-million chance by conducting 20 parity checks [source: Vittorio].
In the next section, we'll look at some of the problems of quantum cryptology.
Quantum Cryptology Problems

Despite all of the security it offers, quantum cryptology also has a few fundamental flaws. Chief among these flaws is the length under which the system will work: Itâ„¢s too short.

Einstein's Spooky Action at a Distance
The original quantum cryptography system, built in 1989 by Charles Bennett, Gilles Brassard and John Smolin, sent a key over a distance of 36 centimeters [source: Scientific American]. Since then, newer models have reached a distance of 150 kilometers (about 93 miles). But this is still far short of the distance requirements needed to transmit information with modern computer and telecommunication systems.

The reason why the length of quantum cryptology capability is so short is because of interference. A photonâ„¢s spin can be changed when it bounces off other particles, and so when it's received, it may no longer be polarized the way it was originally intended to be. This means that a 1 may come through as a 0 -- this is the probability factor at work in quantum physics. As the distance a photon must travel to carry its binary message is increased, so, too, is the chance that it will meet other particles and be influenced by them.

One group of Austrian researchers may have solved this problem. This team used what Albert Einstein called spooky action at a distance. This observation of quantum physics is based on the entanglement of photons. At the quantum level, photons can come to depend on one another after undergoing some particle reactions, and their states become entangled. This entanglement doesnâ„¢t mean that the two photons are physically connected, but they become connected in a way that physicists still don't understand. In entangled pairs, each photon has the opposite spin of the other -- for example, ( / ) and ( ). If the spin of one is measured, the spin of the other can be deduced. Whatâ„¢s strange (or spooky) about the entangled pairs is that they remain entangled, even when theyâ„¢re separated at a distance.

The Austrian team put a photon from an entangled pair at each end of a fiber optic cable. When one photon was measured in one polarization, its entangled counterpart took the opposite polarization, meaning the polarization the other photon would take could be predicted. It transmitted its information to its entangled partner. This could solve the distance problem of quantum cryptography, since there is now a method to help predict the actions of entangled photons.

Even though itâ„¢s existed just a few years so far, quantum cryptography may have already been cracked. A group of researchers from Massachusetts Institute of Technology took advantage of another property of entanglement. In this form, two states of a single photon become related, rather than the properties of two separate photons. By entangling the photons the team intercepted, they were able to measure one property of the photon and make an educated guess of what the measurement of another property -- like its spin -- would be. By not measuring the photonâ„¢s spin, they were able to identify its direction without affecting it. So the photon traveled down the line to its intended recipient none the wiser.

The MIT researchers admit that their eavesdropping method may not hold up to other systems, but that with a little more research, it could be perfected. Hopefully, quantum cryptology will be able to stay one step ahead as decoding methods continue to advance.


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1. Cryptography- an Overview
The purpose of cryptography is to transmit information in such a way that access to it is restricted entirely to the intended recipient, even if the transmission itself is received by others. This science is of increasing importance with the advent of broadcast and network communication, such as electronic transactions, the Internet, e-mail, and cell phones, where sensitive monetary, business, political, and personal communications are transmitted over public channels.
Cryptography operates by a sender scrambling or encrypting the original message or plaintext in a systematic way that obscures its meaning. The encrypted message or crypto text is transmitted, and the receiver recovers the message by unscrambling or decrypting the transmission.
Originally, the security of a cryptogram depended on the secrecy of the entire encrypting and decrypting procedures. Today, however, we use ciphers in which the algorithm for encrypting and decrypting could be revealed to anybody without compromising the security of a particular message. In such ciphers a set of specific parameters, called a key, is used together with the plaintext as an input to the encrypting algorithm, and together with the crypto text as an input to the decrypting algorithm. The encrypting and decrypting algorithms are publicly announced; the security of the cryptogram depends entirely on the secrecy of the key. To prevent this being discovered by accident or systematic search, the key is chosen as a very large number.
Once the key is established, subsequent secure communication can take place by sending crypto text, even over a public channel that is vulnerable to total passive eavesdropping, such as public announcements in mass media. However, to establish the key, two users, who may not be in contact or share any secret information initially, will have to discuss it, using some other reliable and secure channel. But since interception is a set of measurements performed by an eavesdropper on a channel, however difficult this might be from a technological point of view, any classical key distribution can in principle be passively monitored, without the legitimate users realizing that any eavesdropping has taken place.
Cryptographers have tried hard to solve this key distribution problem. The 1970s brought a clever mathematical discovery in the form of public key cryptography (PKC) [1, 2]. The idea of PKC is for each user to randomly choose a pair of mutually inverse transformations that is a scrambling transformation and an unscrambling transformation and to publish the directions for performing the former but not the latter. The transformation is designed so that the unscrambling operation cannot be deduced easily from the scrambling operation, enabling only the user to read scrambled messages. In these systems users do not need to agree on a secret key before they send a message. They work similarly to a drop mailbox with two locks. The owner of the mailbox provides everybody with a key for dropping mail into his box, but only he has the key to open it and read the messages inside.
PKC systems exploit the fact that certain mathematical operations are easier to do in one direction than the other. The systems avoid the key distribution problem, but unfortunately their security depends on unproven mathematical assumptions about the intrinsic difficulty of certain operations. The most popular public key cryptosystem, RSA (Rivest-Shamin-Adleman), gets its security from the difficulty of factoring large numbers [2]. This means that if ever mathematicians or computer scientists come up with fast and clever procedures for factoring large numbers, then the whole privacy and discretion of widespread cryptosystems could vanish overnight. Indeed, recent work in quantum computation suggests that in principle quantum computers might factorize huge integers in practical times, which could jeopardize the secrecy of many modern cryptography techniques [3].
But quantum technology promises to revolutionize secure communication at an even more fundamental level. While classical cryptography relies on the limitations of various mathematical techniques or computing technology to restrict eavesdroppers from learning the contents of encrypted messages, in quantum cryptography the information is protected by the laws of physics. This Hot Topic will discuss some of the basics of how this can be achieved.
2. Classical Cryptography
Cryptography is the art of devising codes and ciphers, and crypto analysis is the art of breaking them. Cryptology is the combination of the two. In the literature of cryptology, information to be encrypted is known as plaintext, and the parameters of the encryption algorithm that transforms the plaintext are collectively called a key. The keys used to encrypt most messages, such as those used to exchange credit-card information over the Internet, are themselves encrypted before being sent [4]. The schemes used to disguise keys are thought to be secure, because discovering them would take too long for even the fastest computers.
Existing cryptographic techniques are usually identified as "traditional" or "modern." Traditional techniques were designed to be simple, for hand encoding and decoding. By contrast, modern techniques use computers, and rely on extremely long keys, convoluted algorithms, and intractable problems to achieve assurances of security.
There are two branches of modern cryptographic techniques: public key encryption and secret key encryption. In PKC, as mentioned above, messages are exchanged using an encryption method so convoluted that even full disclosure of the scrambling operation provides no useful information for how it can be undone. Each participant has a "public key" and a "private key"; the former is used by others to encrypt messages, and the latter is used by the participant to decrypt them.
The widely used RSA algorithm is one example of PKC. Anyone wanting to receive a message publishes a key, which contains two numbers. A sender converts a message into a series of digits, and performs a simple mathematical calculation on the series using the publicly available numbers. Messages are deciphered by the recipient by performing another operation, known only to him [5]. In principle, an eavesdropper could deduce the decryption method by factoring one of the published numbers, but this is chosen to typically exceed 100 digits and to be the product of only two large prime numbers, so that there is no known way to accomplish this factorization in a practical time.
In secret key encryption, a k-bit "secret key" is shared by two users, who use it to transform plaintext inputs to crypto text for transmission and back to plaintext upon receipt. To make unauthorized decipherment more difficult, the transformation algorithm can be carefully designed to make each bit of output depend on every bit of the input. With such an arrangement, a key of 128 bits used for encoding results in a choice of about 1038 numbers. The encrypted message should be secure; assuming that brute force and massive parallelism are employed; a billion computers doing a billion operations per second would require a trillion years to decrypt it. In practice, analysis of the encryption algorithm might make it more vulnerable, but increases in the size of the key can be used to offset this.
The main practical problem with secret key encryption is exchanging a secret key. In principle any two users who wished to communicate could first meet to agree on a key in advance, but in practice this could be inconvenient. Other methods for establishing a key, such as the use of secure courier or private knowledge, could be impractical for routine communication between many users. But any discussion of how the key is to be chosen that takes place on a public communication channel could in principle be intercepted and used by an eavesdropper.
One proposed method for solving this key distribution problem is the appointment of a central key distribution server. Every potential communicating party registers with the server and establishes a secret key. The server then relays secure communications between users, but the server itself is vulnerable to attack. Another method is a protocol for agreeing on a secret key based on publicly exchanged large prime numbers, as in the Diffie Hellman key exchange. Its security is based on the assumed difficulty of finding the power of a base that will generate a specified remainder when divided by a very large prime number, but this suffers from the uncertainty that such problems will remain intractable. Quantum encryption, which will be discussed later, provides a way of agreeing on a secret key without making this assumption.
Communication at the quantum level changes many of the conventions of both classical secret key and public key communication described above. For example, it is not necessarily possible for messages to be perfectly copied by anyone with access to them, or for messages to be relayed without changing them in some respect, nor for an eavesdropper to passively monitor communications without being detected [6].
3. Quantum Cryptography Fundamentals
Electromagnetic waves such as light waves can exhibit the phenomenon of polarization, in which the direction of the electric field vibrations is constant or varies in some definite way. A polarization filter is a material that allows only light of a specified polarization direction to pass. If the light is randomly polarized, only half of it will pass a perfect filter.
According to quantum theory, light waves are propagated as discrete particles known as photons. A photon is a mass less particle, the quantum of the electromagnetic field, carrying energy, momentum, and angular momentum. The polarization of the light is carried by the direction of the angular momentum or spin of the photons. A photon either will or will not pass through a polarization filter, but if it emerges it will be aligned with the filter regardless of its initial state; there are no partial photons. Information about the photon's polarization can be determined by using a photon detector to determine whether it passed through a filter.
"Entangled pairs" are pairs of photons generated by certain particle reactions. Each pair contains two photons of different but related polarization. Entanglement affects the randomness of measurements. If we measure a beam of photons E1 with a polarization filter, one-half of the incident photons will pass the filter, regardless of its orientation. Whether a particular photon will pass the filter is random. However, if we measure a beam of photons E2 consisting of entangled companions of the E1 beam with a filter oriented at 90 degrees to the first filter, then if an E1 photon passes its filter, its E2 companion will also pass its filter. Similarly, if an E1 photon does not pass its filter then its E2 companion will not.
The foundation of quantum cryptography lies in the Heisenberg uncertainty principle, which states that certain pairs of physical properties are related in such a way that measuring one property prevents the observer from simultaneously knowing the value of the other. In particular, when measuring the polarization of a photon, the choice of what direction to measure affects all subsequent measurements. For instance, if one measures the polarization of a photon by noting that it passes through a vertically oriented filter, the photon emerges as vertically polarized regardless of its initial direction of polarization. If one places a second filter oriented at some angle  to the vertical, there is a certain probability that the photon will pass through the second filter as well, and this probability depends on the angle . As  increases, the probability of the photon passing through the second filter decreases until it reaches 0 at  = 90 deg (i.e., the second filter is horizontal). When  = 45 deg, the chance of the photon passing through the second filter is precisely 1/2. This is the same result as a stream of randomly polarized photons impinging on the second filter, so the first filter is said to randomize the measurements of the second.
3.1. Polarization by a filter: Unpolarized light enters a vertically aligned filter, which absorbs some of the light and polarizes the remainder in the vertical direction, which is shown in Figure: 1. A second filter tilted at some angle  absorbs some of the polarized light and transmits the rest, giving it a new polarization.
A pair of orthogonal (perpendicular) polarization states used to describe the polarization of photons, such as horizontal/vertical, is referred to as a basis. A pair of bases are said to be conjugate bases if the measurement of the polarization in the first basis completely randomizes the measurement in the second basis [6], as in the above example with  = 45 deg. It is a fundamental consequence of the Heisenberg uncertainty principle that such conjugate pairs of states must exist for a quantum system.
If a sender, typically designated Alice in the literature, uses a filter in the 0-deg/90-deg basis to give the photon an initial polarization (either horizontal or vertical, but she doesn't reveal which), a receiver Bob can determine this by using a filter aligned to the same basis. However if Bob uses a filter in the 45-deg/135-deg basis to measure the photon, he cannot determine any information about the initial polarization of the photon [7].
These characteristics provide the principles behind quantum cryptography. If an eavesdropper Eve uses a filter aligned with Alice's filter, she can recover the original polarization of the photon. But if she uses a misaligned filter she will not only receive no information, but will have influenced the original photon so that she will be unable to reliably retransmit one with the original polarization. Bob will either receive no message or a garbled one, and in either case will be able to deduce Eve's presence.
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.docx   Q2.docx (Size: 179.68 KB / Downloads: 69)
ABSTRACT
Quantum cryptography uses quantum mechanics to guarantee secure
communication. It enables two parties to produce a shared random bit string known only
to them, which can be used as a key to encrypt and decrypt messages. An important and unique property of quantum cryptography is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental part of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states, a communication system can be implemented which detects eavesdropping. If the level of eavesdropping is below a certain threshold a key can be produced which is guaranteed as secure, otherwise no secure key is possible and communication is aborted.
The security of quantum cryptography relies on the foundations of quantum
mechanics, in contrast to traditional public key cryptography which relies on the
computational difficulty of certain mathematical functions, and cannot provide any
indication of eavesdropping or guarantee of key security.
Quantum cryptography is only used to produce and distribute a key, not to
transmit any message data. This key can then be used with any chosen encryption
algorithm to encrypt and decrypt a message, which can then be transmitted over a
standard communication channel. The algorithm most commonly associated with QKD is
the one-time pad, as it is provably secure when used with a secret, random key.
KEY WORDS: qubit, uncertainty, entanglement, bit commitment, BB84 protocol, Ekert
protocol, key distribution, one-time-pad
INTRODUCTION
Cryptography is the science of keeping private information from unauthorized
access, of ensuring data integrity and authentication, and other tasks. In this survey, we
will focus on quantum-cryptographic key distribution and bit commitment protocols and
we in particular will discuss their security. Before turning to quantum cryptography, let
me give a brief review of classical cryptography, its current challenges and its historical
development.
Two parties, Alice and Bob, wish to exchange messages via some insecure
channel in a way that protects their messages from eavesdropping. An algorithm, which
is called a cipher in this context, scrambles Alice’s message via some rule such that
restoring the original message is hard—if not impossible—without knowledge of the
secret key. This “scrambled” message is called the ciphertext. On the other hand, Bob
(who possesses the secret key) can easily decipher Alice’s ciphertext and obtains her
original plaintext. Figure 1 in this section presents this basic cryptographic scenario.
CLASSICAL CRYPTOGRAPHY
Overviews of classical cryptography can be found in various text books (see, e.g.,
Rothe [2005] and Stinson [2005]). Here, we present just the basic definition of a
cryptosystem and give one example of a classical encryption method, the one-time pad.
DEFENITION
A (deterministic, symmetric) cryptosystem is a five-tuple (P, C, K, E, D)
satisfying the following conditions:
1. P is a finite set of possible plaintexts.
2. C is a finite set of possible ciphertexts.
3. K is a finite set of possible keys.
4. For each k º K, there are an encryption rule ek º E and a corresponding decryption
rule dk º D, where ek: P¨ C and dk : C¨ P are functions satisfying dk (ek (x)) = x
for each plaintext element x º P.
In the basic scenario in cryptography, we have two parties who wish to communicate
over an insecure channel, such as a phone line or a computer network. Usually, these
parties are referred to as Alice and Bob. Since the communication channel is insecure, an
eavesdropper, called Eve, may intercept the messages that are sent over this channel. By
agreeing on a secret key k via a secure communication method, Alice and Bob can make
use of a cryptosystem to keep their information secret, even when sent over the insecure
channel. This situation is illustrated in Figure 1.
The method of encryption works as follows. For her secret message m, Alice uses
the key k and the encryption rule ek to obtain the ciphertext c = ek (m). She sends Bob the
ciphertext c over the insecure channel. Knowing the key k, Bob can easily decrypt the
ciphertext by the decryption rule dk :
dk © = dk (ek (m)) = m.
Knowing the ciphertext c but missing the key k, there is no easy way for Eve to determine
the original message m.
There exist many cryptosystems in modern cryptography to transmit secret
messages. An early well-known system is the one-time pad, which is also known as the
Vernam cipher. The one-time pad is a substitution cipher. Despite its advantageous
properties, which we will discuss later on, the one-time pad’s drawback is the costly
effort needed to transmit and store the secret keys.
ONE-TIME PAD
For plaintext elements in P , we use capital letters and some punctuation marks, which we encode as numbers ranging from 0 to 29, see Figure2.
As is the case with most cryptosystems, the ciphertext space equals the plaintext space.
Furthermore, the key space K also equals P , and we have P =C= K={0, 1, . . . , 29}.
Next, we describe how Alice and Bob use the one-time pad to transmit their messages. A concrete example is shown in Figure 3. Suppose Alice and Bob share a joint secret key k of length n = 12, where each key symbol kiº {0, 1, . . . , 29} is chosen uniformly at random. Let m = m1m2. . . mn be a given message of length n, which Alice wishes to encrypt. For each plaintext letter mi, where 1 ¡Ü i ¡Ü n, Alice adds the plaintext numbers to the key numbers. The result is taken modulo 30. For example, the last letter of the plaintext from Figure 3, “D,” is encoded by “m12=03.” The corresponding key is “m12= 28,” so we have c12= 3 + 28 = 31. Since 31 ß 1 mod 30, our plaintext letter “D” is encrypted as “B.” Decryption works similarly by subtracting, character by character, the key letters from the corresponding ciphertext letters. So the encryption and decryption
can be written as respectively ci= (mi+ ki) mod 30 and mi=(ci- ki) mod 30, 1 ¡Ü i ¡Ü n.
LIMITATIONS
Cryptographic technology in use today relies on the hardness of certain mathematical problems. Classical cryptography faces the following two problems. First,
the security of many classical cryptosystems is based on the hardness of problems such as
integer factoring or the discrete logarithm problem. But since these problems typically
are not provably hard, the corresponding cryptosystems are potentially insecure. For
example, the famous and widely used RSA public-key cryptosystem [Rivest et al. 1978]
could easily be broken if large integers were easy to factor. The hardness of integer
factoring, however, is not a proven fact but rather a hypothesis.1.We mention in passing
that computing the RSA secret key from the corresponding public key is polynomial-time
equivalent to integer factoring [May 2004].
Second, the theory of quantum computation has yielded new methods to tackle
these mathematical problems in a much more efficient way. Although there are still
numerous challenges to overcome before a working quantum computer of sufficient
power can be built, in theory many classical ciphers (in particular public-key cryptosystems such as RSA) might be broken by such a powerful machine. However,
while quantum computation seems to be a severe challenge to classical cryptography in a
possibly not so distant future, at the same time it offers new possibilities to build encryption methods that are safe even against attacks performed by means of a quantum
computer. Quantum cryptography extends the power of classical cryptography by
protecting the secrecy of messages using the physical laws of quantum mechanics.
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21-04-2011, 03:43 PM


.doc   tomkha QC report.doc (Size: 278 KB / Downloads: 46)
ABSTRACT
Quantum cryptography uses quantum mechanics to guarantee secure
communication. It enables two parties to produce a shared random bit string known only
to them, which can be used as a key to encrypt and decrypt messages.
An important and unique property of quantum cryptography is the ability of the
two communicating users to detect the presence of any third party trying to gain
knowledge of the key. This results from a fundamental part of quantum mechanics: the
process of measuring a quantum system in general disturbs the system. A third party
trying to eavesdrop on the key must in some way measure it, thus introducing detectable
anomalies. By using quantum superpositions or quantum entanglement and transmitting
information in quantum states, a communication system can be implemented which
detects eavesdropping. If the level of eavesdropping is below a certain threshold a key
can be produced which is guaranteed as secure, otherwise no secure key is possible and
communication is aborted.
The security of quantum cryptography relies on the foundations of quantum
mechanics, in contrast to traditional public key cryptography which relies on the
computational difficulty of certain mathematical functions, and cannot provide any
indication of eavesdropping or guarantee of key security.
Quantum cryptography is only used to produce and distribute a key, not to
transmit any message data. This key can then be used with any chosen encryption
algorithm to encrypt and decrypt a message, which can then be transmitted over a
standard communication channel. The algorithm most commonly associated with QKD is
the one-time pad, as it is provably secure when used with a secret, random key.
KEY WORDS:
qubit, uncertainty, entanglement, bit commitment, BB84 protocol, Ekert
protocol, key distribution, one-time-pad
1. INTRODUCTION
Cryptography is the science of keeping private information from unauthorized
access, of ensuring data integrity and authentication, and other tasks. In this survey, we
will focus on quantum-cryptographic key distribution and bit commitment protocols and
we in particular will discuss their security. Before turning to quantum cryptography, let
me give a brief review of classical cryptography, its current challenges and its historical
development.
Two parties, Alice and Bob, wish to exchange messages via some insecure
channel in a way that protects their messages from eavesdropping. An algorithm, which
is called a cipher in this context, scrambles Aliceâ„¢s message via some rule such that
restoring the original message is hard”if not impossible”without knowledge of the
secret key. This scrambled message is called the ciphertext. On the other hand, Bob
(who possesses the secret key) can easily decipher Aliceâ„¢s ciphertext and obtains her
original plaintext. Figure 1 in this section presents this basic cryptographic scenario.
Fig. 1. Communication between Alice and Bob, with Eve listening.
But unlike traditional cryptology methods -- encoding and decoding information or messages -- quantum cryptology depends on physics, not mathematics.
In this report, we'll get to the bottom of how quantum encryption works, and how it differs from modern cryptology. But first, we'll look at the uses and the limitations of traditional cryptology methods.
Traditional Cryptology
Photo courtesy NSA
A German Enigma machine

Privacy is paramount when communicating sensitive information, and humans have invented some unusual ways to encode their conversations. In World War II, for example, the Nazis created a bulky machine called the Enigma that resembles a typewriter on steroids. This machine created one of the most difficult ciphers (encoded messages) of the pre-computer age.
Even after Polish resistance fighters made knockoffs of the machines -- complete with instructions on how the Enigma worked -- decoding messages was still a constant struggle for the Allies [source: Cambridge University]. As the codes were deciphered, however, the secrets yielded by the Enigma machine were so helpful that many historians have credited the code breaking as a important factor in the Allies' victory in the war.
What the Enigma machine was used for is called cryptology. This is the process of encoding (cryptography) and decoding (cryptoanalysis) information or messages (called plaintext). All of these processes combined are cryptology. Until the 1990s, cryptology was based on algorithms -- a mathematical process or procedure. These algorithms are used in conjunction with a key, a collection of bits (usually numbers). Without the proper key, it's virtually impossible to decipher an encoded message, even if you know what algorithm to use.
There are limitless possibilities for keys used in cryptology. But there are only two widely used methods of employing keys: public-key cryptology and secret-key cryptology. In both of these methods (and in all cryptology), the sender (point A) is referred to as Alice. Point B is known as Bob.
In the public-key cryptology (PKC) method, a user chooses two interrelated keys. He lets anyone who wants to send him a message know how to encode it using one key. He makes this key public. The other key he keeps to himself. In this manner, anyone can send the user an encoded message, but only the recipient of the encoded message knows how to decode it. Even the person sending the message doesn't know what code the user employs to decode it.
PKC is often compared to a mailbox that uses two keys. One unlocks the front of the mailbox, allowing anyone with a key to deposit mail. But only the recipient holds the key that unlocks the back of the mailbox, allowing only him to retrieve the messages.
The other usual method of traditional cryptology is secret-key cryptology (SKC). In this method, only one key is used by both Bob and Alice. The same key is used to both encode and decode the plaintext. Even the algorithm used in the encoding and decoding process can be announced over an unsecured channel. The code will remain uncracked as long as the key used remains secret.
SKC is similar to feeding a message into a special mailbox that grinds it together with the key. Anyone can reach inside and grab the cipher, but without the key, he won't be able to decipher it. The same key used to encode the message is also the only one that can decode it, separating the key from the message.
Traditional cryptology is certainly clever, but as with all encoding methods in code-breaking history, it's being phased out. Find out why on the next page.
Traditional Cryptology Problems
Both the secret-key and public-key methods of cryptology have unique flaws. Oddly enough, quantum physics can be used to either solve or expand these flaws.
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19-06-2012, 02:33 PM

Quantum Cryptography


.ppt   Quantum Cryptography.ppt (Size: 405.5 KB / Downloads: 24)
what is Quantum Mechanics?

Quantum Mechanics is the study of mechanical systems whose dimensions are close to the atomic scale.
Quantum effects, such as stable electron orbits, entaglement etc.. are not observable on a macroscopic scale, and exist only at the microscopic level.
Applications of Quantum Mechanics range from explaining features of the subatomic world to computational chemistry.
Current research is being done in the fields of Quantum Cryptography, Quantum Computing, and Quantum Teleportation.

Finding Eve

Problem
If an eavesdropper were to gain information about the photons' polarization, the laws of quantum physics dictates that the quantum state of the photons would be altered, thus causing errors in Bob's measurements.
Solution
Alice and Bob compare a subset of remaining bit strings. If more than p bits differ, the key distribution process is aborted and repeated.

Privacy Amplification

As it is impossible to distinguish between eavesdropping and transmission imperfections, a threshhold p (currently 20%) is set for error margins.
If differences occur above the threshhold, privacy amplification can occur.
A new key is created by using Alice and Bob's key to produce a new, shorter key, in such a way that the eavesdropper's knowledge about the new key is negligible.

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