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's
Key |
Value |
Sending
Mode |
Receiving
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.
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