Cryptography – Communication system using cryptography – Fiber optic network
Reexamination Certificate
2000-05-09
2004-10-05
Jung, David (Department: 2134)
Cryptography
Communication system using cryptography
Fiber optic network
C380S255000, C380S041000
Reexamination Certificate
active
06801626
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to secure communication systems and more specifically to distributing key information using quantum cryptography which is unconditionally secure against eavesdropping.
2. Description of the Related Art
Quantum cryptography is known as the powerful technique for secure communication, because it provides unconditional security for distribution of secret key information between remote users. Quantum cryptographic key distribution consists of two parts: quantum information transmissions between legitimate users over a quantum channel and classical information transmission between the legitimate users over a public channel. Any activities of eavesdroppers are detected from the measured results of the two kinds of transmissions, which is ensured from the principles of quantum mechanics such as Heisenberg's uncertainty principle and violation of the Bell theorem. The protocol describes a process whereby the legitimate users determine a secret key while confirming that no eavesdropping is taking place. The security of the secret key is guaranteed by the uncertainty principle whereby disturbance is introduced in the quantum information by any eavesdropping attempt, and hence unconditional security against any wiretapping is achieved. By combining quantum cryptography With a one-time-pad scheme, an unconditional secure communication can be implemented.
A variety of protocols have been proposed so far, for example, the four-state scheme, the two-photon interferometric scheme, the nonorthogonal two-state scheme and the delayed interferometric transmission scheme. One measure of the performance of a protocol is the sensitivity to eavesdropping (specifically, it represents the precision of the amount of information leakage to an eavesdropper determined from the data bit error). Another measure is the data transmission rate which is determined by the reduction of data being discarded or sacrificed for detecting eavesdropping during the protocol. It has been found from the current study that the four-state quantum scheme and the two-photon interferometric scheme are better because of their high sensitivity to eavesdropping and high transmission rate.
The four-state scheme is the first one of the protocols invented. As described in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), C. H. Bennet and G. Brassard, pages 175-179 (Reference
1
), the four-state scheme (currently known as the BB84 protocol) uses a single-photon source
10
(see
FIG. 1
) to produce a pulsed photon carrier
11
for carrying one bit of information, a light modulator
12
, an optical channel
13
for conveying the modulated photon carrier
11
, and a public channel
16
(for which an eavesdropper can access, but cannot alter transmitted messages) for exchanging classical messages between two legitimate users at the sender and receiver sites to test the correlation of the data sent and those actually received. Light modulator
12
modulates the photon carrier
11
and encodes random bit sequence consisting of a bit “0” and a bit “1” produced from a controller
15
onto the photon carrier
11
so that bits “0” and “1” are encoded by two orthogonal polarisation states of a photon. Two nonorthogonal polarisation bases (oil is linear polarisations of 0° and 90° rectilinear basis, and the other is linear polarisations of 45° and 135°; diagonal basis) are used to encode the “0” and “1”. Logical “0” and “1” are encoded with the 0° and 90° polarisations respectively (for rectilinear basis) and the 45° and 135° polarisations respectively (for diagonal basis). Circular polarisations (clockwise and counterclockwise) may be used, instead of one of these two polarisation bases (rectilinear basis or diagonal basis).
Since the 0° polarisations state and 90° polarisation state are orthogonal, photons with such polarisations can be reliably distinguished. A single measurement device
14
at the receiver site that has the ability to distinguish such polarisations is called a rectilinear measurement device. Likewise, photons with 45°-135° linear polarisation can he reliably distinguished by another single measurement device
14
that is called a diagonal measurement device. Quantum mechanical operator, having the eigenstates of rectilinear polarisation states and those having the eigenstate of diagonal basis are non-commuting. Thus, the rectilinear measurement device cannot distinguish the state of the photons which are in the eigenstate of diagonal basis and the diagonal measurement device cannot distinguish the state of the photons which are in the eigenstate of rectilinear basis (they will produce an error with a probability of ½). In particular, when a light pulse contains only one photon, these measurement devices cannot distinguish the state of the photons which are in the eigenstate of rectilinear basis and the state of the photons which are in the eigenstate diagonal basis at the same time (that is the uncertainty principle). The output of the measurement device
14
is supplied to a controller
17
.
The basis (rectilinear basis or diagonal basis) are chosen at random at the sender site when encoding the bit onto the photon carrier. At the receiver site, the basis are also chosen at random independently of the sender site when decoding the modulated carrier. After transmissions of quantum information encoded in the photon carriers over the quantum channel
13
, messages are exchanged over the public channel
16
between the controllers
15
and
17
to test whether both users used the same linear polarisation basis to transmit and receive the data. They discard the data that the legitimate users used a different basis to encode and decode the bit data. The bit value of the remaining data should agree for both legitimate users and are used to obtain the shared key data. An eavesdropper, having no means at all to match his/her polarisation basis to those chosen at the sender and receiver, inevitably produces an error in the shared bit sequence of the legitimate users when he/she attempts to measure the photons to eavesdrop the data. Several bits are then extracted from the shared bit sequence at each site and tested whether they agree by exchanging information over the public channel to determine if eavesdropping is taking place. If the extracted data agreed then the legitimate users find that there is no eavesdropping, and they produce a sequence of common random bits from the remaining data that were not used for this test and use these common random bits as a secret key.
The BB84 protocol is based on the uncertainty principle that in a single quantum system two sets of mutually nonorthogonal bases cannot he measured with certainty at the same time. A given orthogonal basis (e.g., the diagonal basis) can be always represented by a superposition of another basis nonorthogonal to it (e.g., the rectilinear basis). A measurement that can reliably distinguish a given basis would inevitably destroy the superposition state of a given basis (that is, nonorthogonal basis) and cause it to collapse to a given basis. More generally, a measurement that can partially distinguish a given basis would partially destroy the superposition state of given basis and the state after measurement approaches statistical mixture of a given basis.
It is shown in Physical Review Vol. A 56, No. 2, August 1997, Christopher A. Fuchs at al., pages 1163 to 1172 (hereinafter Reference
2
) that the BB84 protocol is equivalent to a procedure in which the presence of an eavesdropper is detected through the collapse of quantum mechanical superposition. Reference
2
shows that the two-photon interferometric scheme is as strong as the four-state quantum cryptography. This two-photon interferometric scheme, known as the E91 protocol, uses the so-called Einstein-Podolsky-Rosen correlation, that is, non-local correlation in the non-separable quantum state of composite system, see Phys
Jung David
NEC Corporation
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