[8460] in cryptography@c2.net mail archive
Re: The Shining Cryptographers Net
daemon@ATHENA.MIT.EDU (John Denker)
Tue Jan 16 11:55:23 2001
Message-Id: <4.2.2.20010116052752.02890f00@127.0.0.1>
Date: Tue, 16 Jan 2001 05:56:13 -0500
To: hal@finney.org
From: John Denker <jsd@research.att.com>
Cc: cryptography@c2.net
In-Reply-To: <200101160635.WAA14338@finney.org>
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At 10:35 PM 1/15/01 -0800, hal@finney.org wrote:
>Here is a rough idea for a quantum-cryptography variant on the DC Net,
>the Dining Cryptographers Net invented by David Chaum.
....
>The photon starts off with vertical polarization. Each cryptographer
>manages a station through which the photon passes, which can be configured
>to either rotate the photon polarization 90 degrees, or to leave it alone.
....
>At the end, the photon polarization is measured by attempting to pass it
>through a vertical polarizer. If it passes, the photon has not been
>rotated, while if it is absorbed, it was rotated. In this way the
>message bit is recovered.
>
>Anonymity derives from the inability of an attacker to measure the photon
>without destroying it, unless he can guess its state.
....
Hmmm. This seems like a mistake in the physics. If the attacker, Eve,
knows that a photon has either vertical (0 degrees) or horizontal (90
degrees) polarization, she can measure it at any point in the ring without
destroying any information, and therefore without risk of detection.
In fancy physics language, these two measurements are
"compatible". Measurement operators can be compatible
a) if they are completely unrelated, or
b) if they are completely correlated.
Case (b) applies here; they are 100% anti-correlated. One can write the
operator equation for projection onto the two polarization states:
P_0 + P_90 = 1
and one can implement this in practice to high accuracy using e.g. a
Brewster-angle beam splitter.
Quantum cryptography relies on measurements of _incompatible_
variables. In this case polarization along a 45-degree axis would be an
example of something incompatible with measurements along the vertical and
horizontal axes.
It may or may not be possible to salvage the underlying idea of "shining
cryptographers" by using 45-degree rotations (not just 90-degree
rotations). Alas I don't immediately see how.
