Quantum Cryptography is the one of the most successul application of quantum computing/information theory.
cryptography is the coding and decoding of secret messages.
Quantum Key Distribution uses the laws of quantum mechanics, we can distribute keys in perfect secrecy.
2. outline
➢Basic Ideas in Cryptography
➢Ideas from the Quantum World
➢Quantum Key Distribution (QKD)
➢BB84 without eavesdropping
➢BB84 with eavesdropping
➢Practical Implementation of QC
➢QKD source
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3. •Introduction
• Quantum cryptography is the one of the
most successful application of Quantum
Computing/InformationTheory.
• For the first time in history, we can use
the forces of nature to implement perfectly secure
cryptosystems.
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4. • Classical Cryptography(RSA) relies heavily
on the complexity of factoring integers.
• FutureQuantumComputers can use Shor’s
Algorithm to efficiently break today’s
cryptosystems.
• Quantum computers can solve factoring
problems in polynomial time.
What happens when that day arrives?
Encrypting is easy.
Codebreaking is hard.
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5. Basic Ideas of Cryptography
• Cryptography: “the coding and
decoding of secret messages.”
•The basic idea is to modify a message so as to make it
unintelligible to anyone but the intended recipient.
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6. Keys and key distribution
• The key is known only to sender and receiver.
• Anyone who knows the key can decrypt the
message.
• Key distribution is the problem of exchanging
the key between sender and receiver.
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7. Perfect Secrecy and OTP
• There exist perfect cryptosystems.
• Example: One-Time Pad (OTP)
• The problem of distributing the keys in the first place
remains.
• Key length has to be same as message length!!
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8. One-time Pad
message: Q U A N T U M
message: 17 (Q) 21 (U) 1 (A) 14 (N) 20 (T) 21 (U) 13 (M)
key: 24 (X) 22 (V) 2 (B) 10 (J) 3 (C) 8 (H) 12 (L)
message + key: 41 (O) 43 (Q) 3 (C) 24 (X) 23 (W) 29 (K) 25 (Y)
ciphertext: O Q C X W K Y
ciphertext – key: 17 (Q) 21 (U) 1 (A) 14 (N) 20 (T) 21 (U) 13 (M)
message: Q U A N T U M
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9. Quantum Key Distribution
• Using the laws of quantum mechanics, we can distribute keys in
perfect secrecy!!
• The Result:The Perfect Cryptosystem.
QC = QKD + OTP
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10. Quantum Physics Basics
• Physical Qubits
• Any subatomic particle can be used to
represent a qubit, e.g. an electron.
• A photon is a convenient choice.
• A photon is an electromagnetic wave.
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11. Polarization
• A photon has a property called polarization, which is the plane in
which the electric field oscillates.
•We can use photons of different polarizations to represent quantum
states:
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12. Ideas from Quantum World
Measurement
• Observing, or measuring, a quantum system will alter its state.
• Example: the Qubit
• When observed, the state of a qubit will collapse to unpredictable
random state 1 or 0.
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13. Polarizers & Basics
• A device called a polarizer allows us to place a photon in a
particular polarization.
•The polarization basis is frame of reference for quantum
measurement.
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14. Polarization of Photons
• Direction of oscillation of the electric field associated to a lightwave
• Polarization states
• What can we do with it ?
E
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18. History of QKD
• StephenWiesner – early 1970s wrote paper "Conjugate
Coding”
• Paper by Charles Bennett and Gilles Brassard in 1984 is
the basis for QKD protocol BB84. Prototype developed in
1991.
• Another QKD protocol was invented independently by
Artur Ekert in 1991.
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19. Two Protocols for QKD
• BB84– uses polarization of photons to encode the bits of
information – relies on “uncertainty” to keep Eve from
learning the secret key.
• Ekert – uses entangled photon states to encode the bits
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20. Quantum Key Distribution
• Quantum Key Distribution exploits the effects discussed in order to
thwart eavesdropping.
• If an eavesdropper uses the wrong polarization basis to measure the
channel, the result of the measurement will be random.
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21. QKD systems
• A QKD system consists of two units which are physically separated at
opposite ends of a pair of communication channels.
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22. BB84
• BB84 was the first security protocol implementingQuantum Key
Distribution.
• It uses the idea of photon polarization.
• The key consists of bits that will be transmitted as photons.
• Each bit is encoded with a random polarization basis!
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23. BB84With no Eavesdropping
• Alice is going to send Bob a key.
• She begins with a random sequence of bits.
• Bits are encoded with a random basis, and then sent to Bob:
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25. BB84With no eavesdropper
• Alice and Bob talk on the public encrypted channel:
• Alice chooses a subset of the bits (the test bits) and reveals which
basis she used to encode them to Bob.
• Bob tellsAlice which basis he used to decode the same bits.
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27. • As long as no errors and/or eavesdropping have occurred, the test
bits should agree.
• Alice and Bob have now made sure that the channel is secure . The
test bits are removed.
• Alice tells Bob the basis she used for the other bits, and they both
have a common set of bits: the final key!
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29. In the presence of eavesdropper
• If an eavesdropper tries to tap the channel, this will automatically
show up in Bob’s measurements.
• In those cases where Alice and Bob have used the same basis, Bob
is likely to obtain an incorrect measurement: Eve’s measurements
are bound to affect the states of the photons.
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31. In the presence of Eavesdropper
• As Eve interceptsAlice’s photons, she has to measure them with a
random basis and send new photons to Bob.
• The photon states cannot be cloned (noncloneability).
• Eve’s presence is always detected: measuring a quantum system
irreparably alters its state.
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33. Entanglement-basedQKD Implementations
• The source at Alice emits an entangled photon pair, with one
photon at 810 nm and the other at 1550 nm.
• The 810 nm photon is measured in four possible polarisation states
(0°, 45°, 90° and 135°) at Alice, using Si APDs.)si avalanche
potodiodes(
• The 1 550 nm photon is sent over the quantum channel (standard
telecom fibro) to Bob, where its polarisation is also analysed along
the four directions using InGaAs APDs(Indium gallium arsenide).
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35. 35
Quantum No-cloningTheorem
• An unknown quantum state CANNOT be cloned.
Therefore, eavesdropper, Eve, cannot have the same
information as Bob.
• Single-photon signals are secure.
a a a
IMPOSSIBLE
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Photon-number splitting attack against multi-photons
A multi-photon signal CAN be split. (Therefore, insecure.)
a
a
Bob
Eve
Splitting attack
aa
Alice
Summary: Single-photon good.
Multi-photon bad.
37. QKD Source
Single-photon source
• A QKD source emits light pulses upon which quantum information is
encoded.
• A source suitable for QKD should possess a property such that the
encoded quantum information can be recovered faithfully through
quantum measurement only when the measurement and encoding
basis are compatible.
• Quantum information can be encoded upon polarisation, phase and
angular momentum. 37
38. • An ideal QKD system would have a perfect single-photon sources
that always emits exactly one photon in response to an applied
trigger.
• Experimental systems that have demonstrated single-photon
emission include single atoms, single ions,and single quantum dots.
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39. • A QKD light source should maintain indistinguishability for qubits in
all degrees of freedom except that of the encoding. In other words, it
should not be possible to discriminate between qubits through
measurement of parameters other than the encoded freedom.
• For example, in the polarisation-encoding BB84 protocol, qubits in
all four states should have exactly the same wavelength, temporal
profile and arrival time, etc. Discrimination of these polarization
encoded qubits can be made possible only through polarisation
measurement. Indistinguishability is a necessary requirement to
prevent information leakage through auxiliary measurements by an
eavesdropper.
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40. Weak Pulses
Weak Laser
• An intensity monitor which integrates the 'single-photon' signals
over time, possessing the necessary sensitivity to determine the
average optical power, can be incorporated after the attenuator.
• Indistinguishability is automatically fulfilled by an attenuated laser
source, since all qubits are prepared by the same emitter and
attenuator.
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42. Entangled-photon sources
• An entanglement-basedQKD system requires the generation and
distribution of entangled photon pairs.
• In this source, photon pair production is achieved by optically
pumping a nonlinear media.The optical excitation can be provided by
a pulsed or continuous-wave laser.
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