CRYPTOLOGY - Hacking: The Art of Exploitation - page 396

through the incorrect filter, its polarization will be randomly modified. This
means that any eavesdropping attempt to measure the polarization of a
photon has a good chance of scrambling the data, making it apparent that
the channel isn't secure.
These strange aspects of quantum mechanics were put to good use by
Charles Bennett and Gilles Brassard in the first and probably best-known
quantum key distribution scheme, called BB84 . First, the sender and receiver
agree on bit representation for the four polarizations, such that each basis
has both 1 and 0. In this scheme, 1 could be represented by both vertical
photon polarization and one of the diagonal polarizations (positive
45 degrees), while 0 could be represented by horizontal polarization and
the other diagonal polarization (negative 45 degrees). This way, 1s and
0s can exist when the rectilinear polarization is measured and when the
diagonal polarization is measured.
Then, the sender sends a stream of random photons, each coming from
a randomly chosen basis (either rectilinear or diagonal), and these photons
are recorded. When the receiver receives a photon, he also randomly chooses
to measure it in either the rectilinear basis or the diagonal basis and records
the result. Now, the two parties publicly compare which basis they used for
each photon, and they keep only the data corresponding to the photons they
both measured using the same basis. This doesn't reveal the bit values of the
photons, since there are both 1s and 0s in each basis. This makes up the key
for the one-time pad.
Since an eavesdropper would ultimately end up changing the polarization
of some of these photons and thus scramble the data, eavesdropping can be
detected by computing the error rate of some random subset of the key. If
there are too many errors, someone was probably eavesdropping, and the
key should be thrown away. If not, the transmission of the key data was secure
and private.

0x714 Computational Security

A cryptosystem is considered to be computationally secure if the best-known
algorithm for breaking it requires an unreasonable amount of computational
resources and time. This means that it is theoretically possible for an eaves-
dropper to break the encryption, but it is practically infeasible to actually do
so, since the amount of time and resources necessary would far exceed the
value of the encrypted information. Usually, the time needed to break a
computationally secure cryptosystem is measured in tens of thousands of
years, even with the assumption of a vast array of computational resources.
Most modern cryptosystems fall into this category.
It's important to note that the best-known algorithms for breaking crypto-
systems are always evolving and being improved. Ideally, a cryptosystem
would be defined as computationally secure if the best algorithm for breaking
it requires an unreasonable amount of computational resources and time,
but there is currently no way to prove that a given encryption-breaking algo-
rithm is and always will be the best one. So, the current best-known algorithm
is used instead to measure a cryptosystem's security.