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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.