Quantum Cryptography

Quantum cryptography, or quantum key distribution (QKD), 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 (i.e. the eavesdropper has no information about), 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.

Quantum cryptography was proposed first by Stephen Wiesner, then at Columbia University in New York, who, in the early 1970s, introduced the concept of quantum conjugate coding. His seminal paper titled "Conjugate Coding" was rejected by IEEE Information Theory but was eventually published in 1983 in SIGACT News (15:1 pp. 78-88, 1983). In this paper he showed how to store or transmit two messages by encoding them in two "conjugate observables", such as linear and circular polarization of light, so that either, but not both, of which may be received and decoded. He illustrated his idea with a design of unforgeable bank notes. A decade later, building upon this work, Charles H. Bennett, of the IBM Thomas J. Watson Research Center, and Gilles Brassard, of the Universite de Montreal, proposed a method for secure communication based on Wiesner's "conjugate observables". In 1990, independently and initially unaware of the earlier work, Artur Ekert, then a Ph.D. student at Wolfson College, University of Oxford, developed a different approach to quantum cryptography based on peculiar quantum correlations known as quantum entanglement

2. Quantum key exchange

Whereas classical public-key cryptography relies on the computational difficulty of certain hard mathematical problems (such as integer factorization) for key distribution, quantum cryptography relies on the laws of quantum mechanics. Quantum cryptographic devices typically employ individual photons of light and take advantage of either the Heisenberg uncertainty principle or quantum entanglement.

Uncertainty: Unlike in classical physics, the act of measurement is an integral part of quantum mechanics. So it is possible to encode information into quantum properties of a photon in such a way that any effort to monitor them disturbs them in some detectable way. The effect arises because in quantum theory, certain pairs of physical properties are complementary in the sense that measuring one property necessarily disturbs the other. This statement is known as the Heisenberg uncertainty principle. The two complementary properties that are often used in quantum cryptography, are two types of photon's polarization, e.g. rectilinear (vertical and horizontal) and diagonal (at 45? and 135?).

Entanglement: It is a state of two or more quantum particles, e.g. photons, in which many of their physical properties are strongly correlated. The entangled particles cannot be described by specifying the states of individual particles and they may together share information in a form which cannot be accessed in any experiment performed on either of the particles alone. This happens no matter how far apart the particles may be at the time.

3. Privacy amplification and information reconciliation

The quantum cryptography protocols described above will provide Alice and Bob with nearly identical shared keys, and also with an estimate of the discrepancy between the keys. These differences can be caused by eavesdropping, but will also be caused by imperfections in the transmission line and detectors. As it is impossible to distinguish between these two types of errors, it is assumed all errors are due to eavesdropping in order to guarantee security.

1. Simon Singh: "The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography "

2. Gilles Van Assche: "Quantum Cryptography and Secret-key Distillation"

3. Kahn, David: "The Codebreakers"

4. Charles H. Bennett, Francois Bessette, Gilles Brassard, Louis Salvail, and John Smolin, "Experimental Quantum Cryptography"

5. Smith, Lawrence Dwight: "Cryptography"

6. http://en.wikipedia.org

7. http://www.cs.dartmouth.edu/~jford/crypto.html

8. http://www.quantenkryptographie.at/

9. http://www.iet.ntnu.no/groups/optics/qcr/