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Background on Quantum Key Distribution

For Immediate Release: April 29, 2004

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Contact: Laura Ost
303-497-4880

Background on Quantum Key Distribution

Quantum encryption systems use lasers to generate individual pulses of light called photons. Each photon is sent in one of two modes, either vertical/horizontal, or plus 45 degrees/minus 45 degrees. Within each mode, one orientation represents the digital value 0, and the other represents the digital value 1. To visualize how this works, imagine that each photon is a tiny envelope moving perpendicular to the ground (vertical=1), parallel to the ground (horizontal=0), tilted at 45 degrees to the right (plus 45 degrees =1) or tilted 45 degrees to the left (minus 45 degrees=0).

The sender, who cryptographers generally call Alice, randomly chooses both a mode and a digital value or orientation for each photon sent over the quantum channel. The receiver, generally called Bob, randomly chooses between the two modes when he tries to detect a photon. This can be visualized as choosing a mailbox slot that accepts only envelopes flying in certain orientations. If he chooses the same mode that Alice used for a particular photon, then Bob always measures the correct orientation, and hence, its digital value. But if he chooses a different mode, then he may get the wrong value for that photon.

To remove this uncertainty, Alice uses another channel—in the NIST system this is a standard wireless Ethernet channel —to tell Bob which mode she used for each photon, but not its digital value. Bob ignores those instances for which he measured a photon in the wrong mode, and tells Alice which ones he measured correctly (but again, not their bit value) so she can also discard the ones Bob did not measure correctly. The correct measurements constitute the encryption key that Alice and Bob now share.

For example, if Alice chooses to send photon number 102 in the vertical/horizontal mode and with the digital value 1, then she orients it vertically and sends it to Bob. If, when the photon arrives at Bob, he chooses the vertical/horizontal mode to measure it, then his measurement will necessarily only show that it is a vertically oriented photon, and he will record a 1. If he uses the plus 45 degree/minus 45 degree mode, then his measurement has an equal chance of yielding a 0 or a 1, but nevertheless he will record the result. After a short time, Alice tells Bob that photon number 102 should have been measured in the vertical/horizontal mode. If he used this mode then he knows his measurement was correct, and he adds the digital value (1, in this example) to his key, and he tells Alice that he measured number 102 correctly so she can keep that value as well. But if he used the other mode, or if the photon never arrived, then he tells Alice to discard the value of that photon.

In real operation, the vast majority of the photons never arrive at Bob. But, as can be seen from the example above, even those that do reach Bob have only a 50/50 chance of being measured in the correct mode. It is only the photons that arrive at Bob, and are measured in the correct mode, that contribute to the key shared by Alice and Bob. Ignoring sources of noise in the channel, at this point Alice's and Bob's keys are identical. (See chart below.) Because the NIST system is capable of sending quantum bits so fast—312 million digital values per second—a large number of photons can be lost or thrown away because Alice and Bob's modes do not match and yet there are still plenty of digital values to produce a secure encryption key.

If someone, referred to by cryptographers as Eve, tries to eavesdrop on the transmission, she will not be able to "read" it without altering it. Eve must randomly position her receiver to intercept Alice's transmission. The photon is converted to electrical energy as it is measured and destroyed, so Eve must generate a new quantum message to send to Bob, but she must guess a significant number of the digital values. These guesses cause errors in the string of digital values used as the encryption key shared by Alice and Bob. By comparing small quantities of their digital key values, Alice and Bob can look for these errors. If they find more differences than can be attributed to known sources, they will know that there is an eavesdropper on the channel and they will discard the key.

Mode Key:

The "+ " symbol represents a vertical or horizontal orientation.
A photon sent in the vertical position equals 1.
A photon sent in the horizontal position equals a 0.

The "X" symbol represents a plus 45 degrees or minus 45 degrees orientation.
A photon sent tilted to the right equals 1.
A photon sent tilted to the left equals a 0.

Alice

Bob

Alice's Key

Value Sending Mode Recieving Mode Measured Result Bob's Key

1

1

+

+

1

1

0

0

+

+

0

0

 

1

X

+

0

 

 

0

X

+

0

 

1

1

X

X

1

1

0

0

X

X

0

0

 

1

X

+

1

 

 

0

X

+

1

 

0

0

+

+

0

0



After transmission, Alice tells Bob which mode was used for each photon. Bob checks the mode used to receive those photons and only saves data where the sending and receiving mode match. Bob tells Alice which photons he received correctly. This string of correctly measured values becomes the encryption key.