07-03-2011, 03:08 PM
PRESENTED BY:
Dr. Janusz Kowalik
[attachment=9704]
Introduction to Quantum Cryptography
Cryptography.
• Transmitting information with access restricted to the intended recipient even if the message is intercepted by others.
• Cryptography is of increasing importance
in our technological age using broadcast, network communications, Internet ,e-mail,
cell phones which may transmit sensitive information related to finances, politics,
business and private confidential matters.
• The process
• Sender
• The classic cryptography
• Encryption algorithm and related key are kept secret.
• Breaking the system is hard due to large numbers of possible keys.
• For example: for a key 128 bits long
• there are
• PKC :the modern cryptography
• In 1970s the Public Key Cryptography emerged.
• Each user has two mutually inverse keys,
• The encryption key is published;
• The decryption key is kept secret.
• Anybody can send a message to Bob
but only Bob can read it.
• RSA
• The most widely used PKC is the RSA algorithm based on the difficulty of
• factoring a product ot two large primes.
• Easy Problem Hard Problem
• Factoring a product of two large primes
• The best known conventional algorithm requires the solution time proportional to:
• Quantum Computing algorithm for factoring.
• In 1994 Peter Shor from the AT&T Bell Laboratory showed that in principle a quantum computer could factor a very long
product of primes in seconds.
• Shor’s algorithm time computational complexity is
• Elements of the Quantum Theory
• Light waves are propagated as discrete quanta called photons.
• They are massless and have energy, momentum and angular momentum called spin.
• Spin carries the polarization.
• If on its way we put a polarization filter
a photon may pass through it or may not.
• We can use a detector to check of a photon has passed through a filter.
• Photon polarization
• Heisenberg Uncertainty Principle
• Certain pairs of physical properties are related in such a way that measuring one property prevents the observer from knowing the value of the other.
When measuring the polarization of a photon, the choice of what direction to measure affects all subsequent measurements.
• If a photon passes through a vertical filter
it will have the vertical orientation regardless of its initial direction of polarization.
• Photon Polarization
• Polarization by a filter
• A pair of orthogonal filters such as vertical/horizontal is called a basis.
• A pair of bases is conjugate if the measurement in the first basis completely randomizes the measurements in the second basis.
• As in the previous slide example for =45deg.
• Sender-receiver of photons
• Suppose Alice uses 0-deg/90-deg polarizer sending photons to Bob. But she does not reveal which.
• Bob can determine photons by using
filter aligned to the same basis.
• But if he uses 45deg/135 deg polarizer to measure the photon he will not be able to determine any information about the initial polarization of the photon.
• The result of his measurement will be completely random
• Eavesdropper Eve
• If Eve uses the filter aligned with Alice’s she can recover the original polarization of the photon.
• If she uses the misaligned filter she will receive no information about the photon .
• Also she will influence the original photon and be unable to retransmit it with the original polarization.
• Bob will be able to deduce Ave’s presence.
• Binary information
• Each photon carries one qubit of information
• Polarization can be used to represent a 0 or 1.
• In quantum computation this is called
qubit.
To determine photon’s polarization the recipient must measure the polarization by ,for example, passing it through a filter.
• Binary information
• A user can suggest a key by sending a stream of randomly polarized photons.
• This sequence can be converted to a binary key.
• If the key was intercepted it could be discarded and a new stream of randomly polarized photons sent.
• The Main contribution of Quantum Cryptography.
• It solved the key distribution problem.
• Unconditionally secure key distribution method proposed by:
• Charles Bennett and Gilles Brassard in 1984.
• The method is called BB84.
• Once key is securely received it can be used to encrypt messages transmitted
by conventional channels.
• Quantum key distribution
• (a)Alice communicates with Bob via a quantum channel sending him photons.
• (b) Then they discuss results using a public channel.
• © After getting an encryption key Bob can encrypt his messages and send them by
any public channel.
• Quantum key distribution
• Both Alice and Bob have two polarizers each.
• One with the 0-90 degree basis (+) and one with 45-135 degree basis ( )
• (a) Alice uses her polarizers to send randomly photons to Bob in one of the four possible polarizations 0,45,90,135 degree.
• (b)
• Example of key distribution
• Security of quantum key distribution
• Quantum cryptography obtains its fundamental security from the fact that each qubit is carried by a single photon, and each photon will be altered as soon as it is read.
• This makes impossible to intercept message without being detected.
• Noise
• The presence of noise can impact detecting attacks.
• Eavesdropper and noise on the quantum channel are indistinguishable.
• (1) Malicious eavesdropper can prevent communication.
• (2) Detecting eavesdropper in the presence of noise is hard.
• State of the Quantum Cryptography technology.
• Experimental implementations have existed since 1990.
• Current (2004) QC is performed over distances of 30-40 kilometers using
optical fiber.
In general we need two capabilities.
(1) Single photon gun.
(2) Being able to measure single photons.
State of the QC technology.
• Efforts are being made to use Pulsed Laser Beam with low intensity for firing single photons.
• Detecting and measuring photons is hard.
• The most common method is exploiting Avalanche Photodiodes in the Geiger mode where single photon triggers a detectable electron avalanche.
State of the QC technology.
• Key transmissions can be achieved for about 80 km distance ( Univ of Geneva 2001).
• (2)For longer distances we can use repeaters. But practical repeaters are a long way in the future.
• Another option is using satellites.
• Richard Hughes at LOS ALAMOS NAT LAB (USA) works in this direction.
• The satellites distance from earth is in hundreds of kilometers.
NIST System
• Uses an infrared laser to generate photons
• and telescopes with 8-inch mirrors to send and receive photons over the air.
• Using the quantum transmitted key
messages were encrypted at the rate
1 million bits per second.
The speed was impressive but the distance between two NIST buildings was only 730 meters.
Commercial QC providers
• id Quantique, Geneva Switzerland
• Optical fiber based system
• Tens of kilometers distances
MagiQ Technologies, NY City
• Optical fiber-glass
• Up to 100 kilometers distances
• NEC Tokyo 150 kilometers
• QinetiQ Farnborough, England
• Through the air 10 kilometers.
• Supplied system to BBN in Cambridge Mass.
Dr. Janusz Kowalik
[attachment=9704]
Introduction to Quantum Cryptography
Cryptography.
• Transmitting information with access restricted to the intended recipient even if the message is intercepted by others.
• Cryptography is of increasing importance
in our technological age using broadcast, network communications, Internet ,e-mail,
cell phones which may transmit sensitive information related to finances, politics,
business and private confidential matters.
• The process
• Sender
• The classic cryptography
• Encryption algorithm and related key are kept secret.
• Breaking the system is hard due to large numbers of possible keys.
• For example: for a key 128 bits long
• there are
• PKC :the modern cryptography
• In 1970s the Public Key Cryptography emerged.
• Each user has two mutually inverse keys,
• The encryption key is published;
• The decryption key is kept secret.
• Anybody can send a message to Bob
but only Bob can read it.
• RSA
• The most widely used PKC is the RSA algorithm based on the difficulty of
• factoring a product ot two large primes.
• Easy Problem Hard Problem
• Factoring a product of two large primes
• The best known conventional algorithm requires the solution time proportional to:
• Quantum Computing algorithm for factoring.
• In 1994 Peter Shor from the AT&T Bell Laboratory showed that in principle a quantum computer could factor a very long
product of primes in seconds.
• Shor’s algorithm time computational complexity is
• Elements of the Quantum Theory
• Light waves are propagated as discrete quanta called photons.
• They are massless and have energy, momentum and angular momentum called spin.
• Spin carries the polarization.
• If on its way we put a polarization filter
a photon may pass through it or may not.
• We can use a detector to check of a photon has passed through a filter.
• Photon polarization
• Heisenberg Uncertainty Principle
• Certain pairs of physical properties are related in such a way that measuring one property prevents the observer from knowing the value of the other.
When measuring the polarization of a photon, the choice of what direction to measure affects all subsequent measurements.
• If a photon passes through a vertical filter
it will have the vertical orientation regardless of its initial direction of polarization.
• Photon Polarization
• Polarization by a filter
• A pair of orthogonal filters such as vertical/horizontal is called a basis.
• A pair of bases is conjugate if the measurement in the first basis completely randomizes the measurements in the second basis.
• As in the previous slide example for =45deg.
• Sender-receiver of photons
• Suppose Alice uses 0-deg/90-deg polarizer sending photons to Bob. But she does not reveal which.
• Bob can determine photons by using
filter aligned to the same basis.
• But if he uses 45deg/135 deg polarizer to measure the photon he will not be able to determine any information about the initial polarization of the photon.
• The result of his measurement will be completely random
• Eavesdropper Eve
• If Eve uses the filter aligned with Alice’s she can recover the original polarization of the photon.
• If she uses the misaligned filter she will receive no information about the photon .
• Also she will influence the original photon and be unable to retransmit it with the original polarization.
• Bob will be able to deduce Ave’s presence.
• Binary information
• Each photon carries one qubit of information
• Polarization can be used to represent a 0 or 1.
• In quantum computation this is called
qubit.
To determine photon’s polarization the recipient must measure the polarization by ,for example, passing it through a filter.
• Binary information
• A user can suggest a key by sending a stream of randomly polarized photons.
• This sequence can be converted to a binary key.
• If the key was intercepted it could be discarded and a new stream of randomly polarized photons sent.
• The Main contribution of Quantum Cryptography.
• It solved the key distribution problem.
• Unconditionally secure key distribution method proposed by:
• Charles Bennett and Gilles Brassard in 1984.
• The method is called BB84.
• Once key is securely received it can be used to encrypt messages transmitted
by conventional channels.
• Quantum key distribution
• (a)Alice communicates with Bob via a quantum channel sending him photons.
• (b) Then they discuss results using a public channel.
• © After getting an encryption key Bob can encrypt his messages and send them by
any public channel.
• Quantum key distribution
• Both Alice and Bob have two polarizers each.
• One with the 0-90 degree basis (+) and one with 45-135 degree basis ( )
• (a) Alice uses her polarizers to send randomly photons to Bob in one of the four possible polarizations 0,45,90,135 degree.
• (b)
• Example of key distribution
• Security of quantum key distribution
• Quantum cryptography obtains its fundamental security from the fact that each qubit is carried by a single photon, and each photon will be altered as soon as it is read.
• This makes impossible to intercept message without being detected.
• Noise
• The presence of noise can impact detecting attacks.
• Eavesdropper and noise on the quantum channel are indistinguishable.
• (1) Malicious eavesdropper can prevent communication.
• (2) Detecting eavesdropper in the presence of noise is hard.
• State of the Quantum Cryptography technology.
• Experimental implementations have existed since 1990.
• Current (2004) QC is performed over distances of 30-40 kilometers using
optical fiber.
In general we need two capabilities.
(1) Single photon gun.
(2) Being able to measure single photons.
State of the QC technology.
• Efforts are being made to use Pulsed Laser Beam with low intensity for firing single photons.
• Detecting and measuring photons is hard.
• The most common method is exploiting Avalanche Photodiodes in the Geiger mode where single photon triggers a detectable electron avalanche.
State of the QC technology.
• Key transmissions can be achieved for about 80 km distance ( Univ of Geneva 2001).
• (2)For longer distances we can use repeaters. But practical repeaters are a long way in the future.
• Another option is using satellites.
• Richard Hughes at LOS ALAMOS NAT LAB (USA) works in this direction.
• The satellites distance from earth is in hundreds of kilometers.
NIST System
• Uses an infrared laser to generate photons
• and telescopes with 8-inch mirrors to send and receive photons over the air.
• Using the quantum transmitted key
messages were encrypted at the rate
1 million bits per second.
The speed was impressive but the distance between two NIST buildings was only 730 meters.
Commercial QC providers
• id Quantique, Geneva Switzerland
• Optical fiber based system
• Tens of kilometers distances
MagiQ Technologies, NY City
• Optical fiber-glass
• Up to 100 kilometers distances
• NEC Tokyo 150 kilometers
• QinetiQ Farnborough, England
• Through the air 10 kilometers.
• Supplied system to BBN in Cambridge Mass.
