Cryptography Reference
In-Depth Information
quantum physics (instead of information theory). More specifically, quantum cryp-
tography makes use and takes advantage of the
Heisenberg uncertainty principle
of quantum physics to provide a secure quantum channel. Roughly speaking, the
Heisenberg uncertainty principle states that certain pairs of physical properties are
related in such a way that measuring one property prevents an adversary from si-
multaneously knowing the value of the other. In particular, when measuring the
polarization of a photon, the choice of what direction to measure affects all mea-
surements. For example, suppose you measure the polarization of a photon using
a vertical filter. Classically, you would assume that if the photon passes through, it
is vertically polarized, and therefore if you placed in front of the photon another
filter with some angle
t
to the vertical, then the photon would not pass through.
However, quantum mechanics states that, in fact, there is a certain probability that
the photon passes through the second filter as well, and this probability depends
on the angle
t
.As
t
increases, the probability of the photon passing through the
second filter decreases until it reaches 0 at
t
=90deg (i.e., the second filter is
horizontal). When
t
=45deg, the chance of the photon passing through the second
filter is exactly 1
/
2. In measuring the polarization of photons, we refer to a pair of
orthogonal polarization states, such as 0 deg and 90 deg or 45 deg and 135 deg, as a
(polarization)
basis
. A pair of bases is said to be
conjugate
if the measurement of the
polarization in the first basis completely randomizes the measurement in the second
basis (as in the previous example above with
t
=45deg). Consequently, the 0
/
90-
deg and 45
/
135-deg bases are conjugate. Note that if someone else gives the photon
an initial polarization (either horizontal or vertical, but you don't know which) and
you use a filter in the 45
/
135-deg basis to measure the photon, you cannot determine
any information about the initial polarization of the photon.
As further explained later, these principles can be used to establish a quantum
channel that cannot be attacked passively without detection, meaning that the
fact that someone is trying to eavesdrop on the channel can be detected by the
communicating entities. In fact, the adversary cannot gain even partial information
about the data being transmitted without altering it in a random and uncontrollable
way that is likely to be detected. As such, the quantum channel can be used to
transmit secret information or to agree on a secret key. It cannot be used, however,
to implement digital signatures and to provide nonrepudiation services accordingly.
Anyway, the quantum channel is provably secure even against an opponent with
superior technology and unlimited computational power (and even if
).
The field of quantum cryptography was pioneered by Stephen Wiesner in the
early 1970s [9]. Wiesner had two applications in mind:
P
=
NP
•
Making money that is impossible to counterfeit;
