Cryptography Reference
In-Depth Information
•
Multiplexing two or three messages in such a way that reading one destroys
the other(s).
The first feasible quantum cryptosystems were designed in the early 1980s by
Charles H. Bennett and Gilles Brassard [10]. The most important quantum cryp-
tosystem is the quantum key exchange (see Section 16.4.2). Their first apparatus
that implemented a quantum key exchange was capable of transmitting a secret key
over a distance of approximately 30 cm. Note that a major disadvantage of quantum
cryptography in practice is the fact that quantum transmissions are necessarily weak
and cannot be amplified in transit (an amplifier is like an adversary from a quantum
system's perspective). This severely limits the distance that can be overcome with a
quantum channel. Since the early work of Bennett and Brassard, many researchers
have turned towards quantum cryptography
2
and many improvements have been
made. In 1993, for example, a 10 km quantum channel was built, and today it
is possible to overcome a distances of 67 km.
3
Furthermore, many other quantum
cryptographic protocols have been developed and proposed, such as quantum pro-
tocols for oblivious transfer and bit commitment (again, refer to the bibliography of
quantum cryptography referenced in footnote 2).
16.4.2
Quantum Key Exchange Protocol
Let A be the sender and B the receiver on a quantum channel. A may send out
photons in one of four polarizations: 0, 45, 90, or 135 deg (we use the symbols
−→
to refer to these polarizations). At the other end of the quantum
channel, B is to measure the polarizations of the received photons. According to the
laws of quantum mechanics, the receiving device can distinguish between rectilinear
polarizations (i.e., 0 and 90 deg), or it can quickly be reconfigured to discriminate
between diagonal polarizations (i.e., 45 and 135 deg); it cannot, however, distinguish
both types of polarization simultaneously (this is because the rectilinear and diagonal
polarizations' bases are conjugate, meaning that the measurement of the polarization
in the first basis completely randomizes the measurement in the second basis).
In this setting, A and B can use the quantum key exchange protocol proposed
by Bennett and Brassard to agree on a shared secret key. In a first step, A chooses
a random bitstring and a random sequence of polarization bases (i.e., rectilinear or
diagonal). A sends B a sequence of photons, each representing one bit of the bitstring
in the polarization basis chosen for that bit position. For example, a horizontal or
45-deg photon can be used to represent a zero, whereas a vertical or 135-deg photon
,
,
↑
,and
2
Refer to http://www.cs.mcgill.ca/˜crepeau/CRYPTO/Biblio-QC.html for a bibliography of quantum
cryptography.
3
The company id Quantique SA (http://www.idquantique.com) is selling corresponding devices.
