[51] in cryptography@c2.net mail archive
Re: Multi-drop quantum cryptography article in Nature 385, 47-49 (1997)
daemon@ATHENA.MIT.EDU (Hal Finney)
Tue Jan 14 16:15:40 1997
Date: Tue, 14 Jan 1997 11:16:53 -0800
From: Hal Finney <hal@rain.org>
To: cryptography@c2.net
One problem with quantum crypto is that the immunity to eavesdroppers
is not perfect.
Consider the canonical quantum crypto scheme: Alice sends to Bob
photons which are either + or X polarized (that is, either polarized
vertically-vs-horizontally, or polarized in one of the two diagonal
directions). For each one, Bob sets his polarization detector to
either the + or X position. If he guesses the same as what Alice sends,
he correctly observes the polarization. After they exchane some bits
this way, he tells Alice what his settings were and she says which ones
matched hers, so they use those results.
If Eve in the middle is trying to read the photons, she too has to set
her detector to + or X. Then she will send on a photon polarized in
the form that she read. If she guesses right, her change will be
undetectable. The photon she sends on will be the same as what Alice
sent. If she guesses wrong, she will have changed the photon, but Bob
will still have a 1/2 chance of getting the right measurement assuming
he has his polarizer set the same as what Alice sent.
So, half the photons Eve reads will be undetectable. 1/4 will be
altered, but Bob will have his detector set wrong so they won't be
used. 1/8 will be altered but Bob will get the right reading anyway
by luck. Only 1/8 will actually be detected as being changed.
This means that Eve can hope to detect a few photons without being
detected. If she knows the signal/noise ratio of Alice and Bob's equipment,
she can keep the threshold of extra errors she introduces within the
reasonable range of existing noise. Depending on how high this is,
she may be able to acquire a significant number of bits without being
detected.
Hal
