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handofg0d Posted:

Example: Intercept and resend

The simplest type of possible attack is the intercept-resend attack, where Eve measures the quantum states (photons) sent by Alice and then sends replacement states to Bob, prepared in the state she measures. In the BB84 protocol this will produce errors in the key shared between Alice and Bob. As Eve has no knowledge of the basis a state sent by Alice is encoded in, she can only guess which basis to measure in, in the same way as Bob. If she chooses correctly then she will measure the correct photon polarization state as sent by Alice, and will resend the correct state to Bob. However if she chooses incorrectly then the state she measures will be random, and the state sent to Bob will not be the same as the state sent by Alice. If Bob then measures this state in the same basis Alice sent he will get a random result, as Eve has sent him a state in the opposite basis, instead of the correct result he would get without the presence of Eve. An example of this type of attack is shown in the table below.

Alice’s random bit 0 1 1 0 1 0 0 1

Alice’s random sending basis

Photon polarization Alice sends

Eve’s random measuring basis

Polarization Eve measures and sends

Bob’s random measuring basis

Photon polarization Bob measures

PUBLIC DISCUSSION OF BASIS

Shared secret key 0 0 0 1

Errors in key ✓ ✘ ✓ ✓

The probability Eve chooses the incorrect basis is 50% (bumuming Alice chooses her basis randomly), and if Bob measures this intercepted photon in the basis Alice sent he will get a random result, i.e. an incorrect result with probability of 50%. The probability an intercepted photon generates an error in the key string is then 50% x 50% = 25%. If Alice and Bob publicly compare n of their key bits (thus discarding them as key bits, as they are no longer secret) the probability they find disagreement and identify the presence of Eve is

P_d = 1 – \left(\frac{3}{4}\right)^n

So to detect an eavesdropper with probability Pd = 0.999999999 Alice and Bob need to compare n = 72 key bits.

[edit] Security Proofs

The above is just a simple example of an attack. If Eve is bumumed to have unlimited resources, for example clbumical and quantum computing power, there are many more attacks possible. BB84 has been proven secure against any attacks allowed by quantum mechanics, both for sending information using an ideal photon source which only ever emits a single photon at a time[12], and also using practical photon sources which sometimes emit multiphoton pulses[13]. These proofs are unconditionally secure in the sense that no conditions are imposed on the resources available to the Eavesdropper, however there are other conditions required:

1. Eve cannot access Alice and Bob’s encoding and decoding devices.

2. The random number generators used by Alice and Bob must be trusted and truly random (for example a Quantum random number generator).

3. The clbumical communication channel must be authenticated using an unconditionally secure authentication scheme.

[edit] Man in the middle attack

Quantum cryptography is vulnerable to a man-in-the-middle attack when used without authentication to the same extent as any clbumical protocol, since no known principle of quantum mechanics can distinguish friend from foe. As in the clbumical case, Alice and Bob cannot authenticate each other and establish a secure connection without some means of verifying each other’s identities (such as an initial shared secret). If Alice and Bob have an initial shared secret then they can use an unconditionally secure authentication scheme (such as Carter-Wegman,[14]) along with quantum key distribution to exponentially expand this key, using a small amount of the new key to authenticate the next session[15]. Several methods to create this initial shared secret have been proposed, for example using a 3rd party[16] or chaos theory[17].

[edit] Photon number splitting attack

In the BB84 protocol Alice sends quantum states to Bob using single photons. In practice many implementations use laser pulses attenuated to a very low level to send the quantum states. These laser pulses contain a very small number of photons, for example 0.2 photons per pulse, which are distributed according to a Poissonian distribution. This means most pulses actually contain no photons (no pulse is sent), some pulses contain 1 photon (which is desired) and a few pulses contain 2 or more photons. If the pulse contains more than one photon, then Eve can split off the extra photons and transmit the remaining single photon to Bob. This is the basis of the photon number splitting attack[18], where Eve stores these extra photons in a quantum memory until Bob detects the remaining single photon and Alice reveals the encoding basis. Eve can then measure her photons in the correct basis and obtain information on the key without introducing detectable errors.

Even with the possibility of a PNS attack a secure key can still be generated, as shown in the GLLP security proof[13], however a much higher amount of privacy amplification is needed reducing the secure key rate significantly (with PNS the rate scales as t2 as compared to t for a single photon sources, where t is the transmittance of the quantum channel).

There are several solutions to this problem. The most obvious is to use a true single photon source instead of an attenuated laser. While such sources are still at a developmental stage QKD has been carried out successfully with them[19]. However as current sources operate at a low efficiency and frequency key rates and transmission distances are limited. Another solution is to modify the BB84 protocol, as is done for example in the SARG04 protocol[20], in which the secure key rate scales as t3 / 2. The most promising solution is the decoy state idea[21], in which Alice randomly sends some of her laser pulses with a lower average photon number. These decoy states can be used to detect a PNS attack, as Eve has no way to tell which pulses are signal and which decoy. Using this idea the secure key rate scales as t, the same as for a single photon source. This idea has been implemented successfully in several QKD experiments[22], allowing for high key rates secure against all known attacks.

[edit] Hacking attacks

Hacking attacks target imperfections in the implementation of the protocol instead of the protocol directly. If the equipment used in quantum cryptography can be tampered with, it could be made to generate keys that were not secure using a random number generator attack. Another common clbum of attacks is the Trojan horse attack[23] which does not require physical access to the endpoints: rather than attempt to read Alice and Bob’s single photons, Mallory sends a large pulse of light back to Alice in between transmitted photons. Alice’s equipment reflects some of Mallory’s light, revealing the state of Alice’s polarizer. This attack is easy to avoid, for example using an optical isolator to prevent light from entering Alice’s system, and all other hacking attacks can similarly be defeated by modifying the implementation. Apart from Trojan horse there are several other known attacks including faked state attacks [24], phase remapping attacks [25] and time-shift attacks [26]. The time-shift attack has even been successfully demonstrated on a commercial quantum crypto-system [27]. This demonstration is the first successful demonstration of quantum hacking against a non-homemade quantum key distribution system.

[edit] Denial of service

Because currently a dedicated fibre optic line (or line of sight in free space) is required between the two points linked by quantum cryptography, a denial of service attack can be mounted by simply cutting or blocking the line or, perhaps more surreptitiously, by attempting to tap it.

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The highest bit rate system currently demonstrated exchanges secure keys at 1 Mbit/s (over 20 km of optical fibre) and 10 kbit/s (over 100 km of fibre), achieved by a collaboration between the University of Cambridge and Toshiba using the BB84 protocol with decoy pulses[5].

As of March 2007[update] the longest distance over which quantum key distribution has been demonstrated using optic fibre is 148.7 km, achieved by Los Alamos/NIST using the BB84 protocol[6]. Significantly, this distance is long enough for almost all the spans found in today’s fibre networks. The distance record for free space QKD is 144 km between two of the Canary Islands, achieved by a European collaboration using entangled photons (the Ekert scheme) in 2006[7], and using BB84 enhanced with decoy states[8] in 2007 [9]. The experiments suggest transmission to satellites is possible, due to the lower atmospheric density at higher altitudes. For example although the minimum distance from the International Space Station to the ESA Space Debris Telescope is about 400 km, the atmospheric thickness is about an order of magnitude less than in the European experiment, thus yielding less attenuation compared to this experiment.

The DARPA Quantum Network[10], a 10-node quantum cryptography network, has been running since 2004 in Mbumachusetts, USA. It is being developed by BBN Technologies, Harvard University, Boston University and QinetiQ.

There are currently four companies offering commercial quantum cryptography systems; id Quantique (Geneva), MagiQ Technologies (New York), SmartQuantum (France) and Quintessence Labs (Australia). Several other companies also have active research programmes, including Toshiba, HP, IBM, Mitsubishi, NEC and NTT (See External links for direct research links).

Quantum encryption technology provided by the Swiss company Id Quantique was used in the Swiss canton (state) of Geneva to transmit ballot results to the capitol in the national election occurring on Oct. 21, 2007.[10]

In 2004, the world’s first bank transfer using quantum cryptography was carried in Vienna, Austria. An important cheque, which needed absolute security, was transmitted from the Mayor of the city to an Austrian bank.[11]

The world’s first computer network protected by quantum cryptography was implemented in October 2008, at a scientific conference in Vienna. The network used 200 km of standard fibre optic cable to interconnect six locations across Vienna and the town of St Poelten located 69 km to the west. The event was witnessed by Gilles Brbumard and Anton Zeilinger. [11]

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handofg0d Posted:

BB84 protocol: Charles H. Bennett and Gilles Brbumard (1984)

This protocol, known as BB84 after its inventors and year of publication, was originally described using photon polarization states to transmit the information. However, any two pairs of conjugate states can be used for the protocol, and many optical fibre based implementations described as BB84 use phase encoded states. The sender (traditionally referred to as Alice) and the receiver (Bob) are connected by a quantum communication channel which allows quantum states to be transmitted. In the case of photons this channel is generally either an optical fibre or simply free space. In addition they communicate via a public clbumical channel, for example using broadcast radio or the internet. Neither of these channels need to be secure; the protocol is designed with the bumumption that an eavesdropper (referred to as Eve) can interfere in any way with both.

The security of the protocol comes from encoding the information in non-orthogonal states. Quantum indeterminacy means that these states cannot in general be measured without disturbing the original state (see No cloning theorem). BB84 uses two pairs of states, with each pair conjugate to the other pair, and the two states within a pair orthogonal to each other. Pairs of orthogonal states are referred to as a basis. The usual polarization state pairs used are either the rectilinear basis of vertical (0°) and horizontal (90°), the diagonal basis of 45° and 135° or the circular basis of left- and right-handedness. Any two of these bases are conjugate to each other, and so any two can be used in the protocol. Below the rectilinear and diagonal bases are used.

Basis 0 1

The first step in BB84 is quantum transmission. Alice creates a random bit (0 or 1) and then randomly selects one of her two bases (rectilinear or diagonal in this case) to transmit it in. She then prepares a photon polarization state depending both on the bit value and basis, as shown in the table to the left. So for example a 0 is encoded in the rectilinear basis (+) as a vertical polarization state, and a 1 is encoded in the diagonal basis (x) as a 135° state. Alice then transmits a single photon in the state specified to Bob, using the quantum channel. This process is then repeated from the random bit stage, with Alice recording the state, basis and time of each photon sent.

Quantum mechanics (particularly quantum indeterminacy) says there is no possible measurement that will distinguish between the 4 different polarization states, as they are not all orthogonal. The only measurement possible is between any two orthogonal states (a basis), so for example measuring in the rectilinear basis will give a result of horizontal or vertical. If the photon was created as horizontal or vertical (as a rectilinear eigenstate) then this will measure the correct state, but if it was created as 45° or 135° (diagonal eigenstates) then the rectilinear measurement will instead return either horizontal or vertical at random. Furthermore, after this measurement the photon will be polarized in the state it was measured in (horizontal or vertical), with all information about its initial polarization lost.

As Bob does not know the basis the photons were encoded in, all he can do is select a basis at random to measure in, either rectilinear or diagonal. He does this for each photon he receives, recording the time, measurement basis used and measurement result. After Bob has measured all the photons, he communicates with Alice over the public clbumical channel. Alice broadcasts the basis each photon was sent in, and Bob the basis each was measured in. They both discard photon measurements (bits) where Bob used a different basis, which will be half on average, leaving half the bits as a shared key.

Alice’s random bit 0 1 1 0 1 0 0 1

Alice’s random sending basis

Photon polarization Alice sends

Bob’s random measuring basis

Photon polarization Bob measures

PUBLIC DISCUSSION OF BASIS

Shared secret key 0 1 0 1

To check for the presence of eavesdropping Alice and Bob now compare a certain subset of their remaining bit strings. If a third party (usually referred to as Eve, for ‘eavesdropper’Log in to see images!

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handofg0d Posted:

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 aspect 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 that is guaranteed to be 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 bumociated with QKD is the one-time pad, as it is provably secure when used with a secret, random key.[1]

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handofg0d Posted:

A photon is often referred to as a “light quantum”. The energy of an electron bound to an atom (at rest) is said to be quantized, which results in the stability of atoms, and of matter in general. But these terms can be a little misleading, because what is quantized is this Planck’s constant quantity whose units can be viewed as either energy multiplied by time or momentum multiplied by distance.

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Odalisque Posted:

This second step was only possible due to a certain amount of luck (or skill, even though Planck himself called it “a fortuitous guess at an interpolation formula”Log in to see images!. It was during the course of polishing the mathematics of his formula that Planck stumbled upon the beginnings of Quantum Theory. Briefly stated, he had two mathematical expressions:

* (i) from the previous work on the red parts of the spectrum, he had x;

* (ii) now, from the new infrared data, he got x².

Combining these as x(a+x), he still has x, approximately, when x is much smaller than a (the red end of the spectrum); but now also x² (again approximately) when x is much larger than a (in the infrared). The formula for the energy E, in a single mode of radiation at frequency λ, and temperature T, can be written

E = \frac{h \lambda}{e^{\frac{h \lambda}{k T}} – 1}

This is (essentially) what is being compared with the experimental measurements. There are two parameters to determine from the data, written in the present form by the symbols used today: h is the new Planck’s constant, and k is Boltzmann’s constant. Both have now become fundamental in physics, but that was by no means the case at the time. The “elementary quantum of energy” is hλ. But such a unit does not normally exist, and is not required for quantization.

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handofg0d Posted:

When a body is heated, it emits radiant heat, a form of electromagnetic radiation in the infrared region of the EM spectrum. All of this was well understood at the time, and of considerable practical importance. When the body becomes red-hot, the red wavelength parts start to become visible. This had been studied over the previous years, as the instruments were being developed. However, most of the heat radiation remains infrared, until the body becomes as hot as the surface of the Sun (about 6000 K or 5726 °C, where most of the light is white in color). This was not achievable in the laboratory at that time. What is more, measuring specific infrared wavelengths was only then becoming feasible, due to newly developed experimental techniques. Until then, most of the electromagnetic spectrum was not measurable, and therefore blackbody emission had not been mapped out in detail.