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QUANTUM CRYPTOGRAPHY
Introduction to Cryptography:
• The science of keeping private information from unauthorized access
ensuring data integrity and authentication.
• Lets assume Alice and Bob wish to exchange messages via some
channel in a way that they protect their messages from
eavesdropping.
• An algorithm, which is called a cipher in this context, scrambles Alice’s
message via some rule such that restoring the original message is
hard—if not impossible—without knowledge of the secret key.
• The scrambled text is called the cipher text.
Continued:
• On the other hand, Bob can
easily decipher Alice’s
chiphertext and obtain
plaintext. The following figure
describes the overall scenario
including the presence of
eavesdropper.
Basic ideology and Terms 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.
• For message (plaintext) M, e(M, K) encryption - ciphertext d[e(M, K),
K] = M decryption.
• Cryptosystem (Cipher System) – method of disguising messages so
that only certain people can read them
Continued:
• Cryptography – Art of creating and
using Cryptosystems.
• Cryptanalysis – Art of breaking
Cryptosystems.
• Cryptography – study of Cryptography
and Cryptosystems.
Key and Key Distribution:
• K is the key.
• The key is known to sender
and receiver and it is secret.
• Anyone who knows the key
can decrypt the message.
• Key distribution is the
problem of exchanging the
key between sender and
receiver.
One Time Pad
• An early well-known cryptosystem is the one-time pad, which is also
known as the Vernam cipher.
• The one-time pad is a substitution cipher.
• the one-time pad’s drawback is the costly effort needed to transmit
and store the secret keys.
fig (a): Encryption and decryption example for the one-time
pad
Need of Quantum Cryptography:
• Classical Cryptography relies heavily on the complexity of factoring
integers.
• Quantum Computers can use Shor’s Algorithm to efficiently break
today’s cryptosystems.
• We need a new kind of cryptography!
Quantum Cryptography:
• Quantum cryptography is the single most successful application of Quantum
Computing/Information Theory.
• For the first time in history, we can use the forces of nature to implement
perfectly secure cryptosystems.
• It is the science of exploiting the quantum mechanical properties to perform
cryptographic tasks.
• Its main advantage is that it allows the completion of various cryptographic
tasks that are proven or assume to be impossible using only classical
communication.
History:
• Quantum cryptography is based on 2 major elements of quantum mechanics
as the base of its implementation.
• 1) Heisenberg uncertainty principle: At the instant at which the position of
the electron is known, its momentum therefore can be known only up to
magnitudes which correspond to that discontinuous change; thus, the more
precisely the position is determined, the less precisely the momentum is
known, and conversely.
• 2)Principle of photon polarization: It is the quantum mechanical description
of the classical polarized sinusoidal plane electromagnetic wave. An individual
photon can be described as having right or left circular polarization or a
superposition of two.
Another Principle of Quantum Cryptography:
• The No Cloning Theorem: It states that it is impossible to create a
copy of an arbitrary unknown quantum state. This makes it
impossible to perform eavesdropping because it will quickly be
detected and thus guarantees that the communicated data remains
private.
Quantum Key Distribution:
• Quantum Key Distribution exploits the effects discussed in order to
thwart eavesdropping.
• It enables two parties to produce a shared random bit string known only
to them, which can be used as a key for encryption and decryption.
• If an eavesdropper uses the wrong polarization basis to measure the
channel, the result of the measurement will be random.
QKD Components:
• A fiber or free-space quantum channel to send quantum states of light
between the transmitter (Alice) and receiver (Bob). This channel does not
need to be secured.
• A public but authenticated communication link between the two parties to
perform post-processing steps and distill a correct and secret key.
• A key exchange protocol that exploits quantum properties to ensure
security by detecting eavesdropping or errors, and by calculating the
amount of information that has been intercepted or lost. Both errors and
potential information leakage are removed during subsequent error
correction and privacy amplification post-processing steps, leaving Bob and
Alice with a shared key known only to them.
Types of Quantum Key Distribution:
• 1. Discrete variable QKD: It encodes quantum information in discrete
variables and uses single photon detectors to measure the received
quantum states. Example: BB84 and E91 protocols.
• 2. Contiguous variable QKD: IN this the quantum information is encoded
onto the amplitude and phase quadratures of a coherent laser and then
can be measured by the receiver using homodyne detectors.
• Both these approaches have been proven to be information theoretically
secure even in the presence of an attacker or eavesdropper.
QKD Protocols:
• A protocol is a set of rules governing the exchange of messages over a
channel.
• A security protocol is a special protocol designed to ensure security
properties are met during communications.
• There are three main security protocols for QKD: BB84, B92, and
Entanglement-Based QKD.
BB84 Protocol
• BB84 was the first security protocol implementing Quantum 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!
• BB84 with no eavesdropping • Bob receives the photons and must
decode them using a random basis.
• Photon Basis? + + × + × Bit? 0 0 0 1 1 Some of his measurements are
correct.
Continued:
• BB84 with no eavesdropping:
• Bob receives the photons and must decode them using a random basis.
• In the below figure some of his measurements are correct.
• As long as no errors 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.
B92 Protocol
• Similar to BB84 but uses only 2 out of 4 BB84 state, which makes it easy
to implement.
• It encodes classical bits in two non orthogonal states. Since no
measurement can distinguish two non orthogonal quantum states, it
makes it impossible to identify the bit with certainty.
• If there is any attempt to learn the bit, it will modify the state in a
noticeable way. B92 allows a receiver to learn whenever he gets the bit
sent without further discussion with Alice.
• In B92, the classical bit b=0 is encoded by a photon with horizontal
polarization and b=1 is encoded by photon with polarization angle 45
degrees.
Theoretical threats to Quantum cryptography
• A hacker can blind a detector with a strong pulse, rendering it unable to
see the secret keeping photons.
• photons are often generated using a laser tuned to such a low intensity
that its producing one single photon at a time.
• There is a certain probability that the laser will make a photon encoded
with your secret information and then a second photon with that same
information. All an intruder has to do is to steal that second photon and
could gain access to the data.

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quantumcryptography-180425230158.pdf

  • 2. Introduction to Cryptography: • The science of keeping private information from unauthorized access ensuring data integrity and authentication. • Lets assume Alice and Bob wish to exchange messages via some channel in a way that they protect their messages from eavesdropping. • An algorithm, which is called a cipher in this context, scrambles Alice’s message via some rule such that restoring the original message is hard—if not impossible—without knowledge of the secret key. • The scrambled text is called the cipher text.
  • 3. Continued: • On the other hand, Bob can easily decipher Alice’s chiphertext and obtain plaintext. The following figure describes the overall scenario including the presence of eavesdropper.
  • 4. Basic ideology and Terms 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. • For message (plaintext) M, e(M, K) encryption - ciphertext d[e(M, K), K] = M decryption. • Cryptosystem (Cipher System) – method of disguising messages so that only certain people can read them
  • 5. Continued: • Cryptography – Art of creating and using Cryptosystems. • Cryptanalysis – Art of breaking Cryptosystems. • Cryptography – study of Cryptography and Cryptosystems.
  • 6. Key and Key Distribution: • K is the key. • The key is known to sender and receiver and it is secret. • Anyone who knows the key can decrypt the message. • Key distribution is the problem of exchanging the key between sender and receiver.
  • 7. One Time Pad • An early well-known cryptosystem is the one-time pad, which is also known as the Vernam cipher. • The one-time pad is a substitution cipher. • the one-time pad’s drawback is the costly effort needed to transmit and store the secret keys. fig (a): Encryption and decryption example for the one-time pad
  • 8. Need of Quantum Cryptography: • Classical Cryptography relies heavily on the complexity of factoring integers. • Quantum Computers can use Shor’s Algorithm to efficiently break today’s cryptosystems. • We need a new kind of cryptography!
  • 9. Quantum Cryptography: • Quantum cryptography is the single most successful application of Quantum Computing/Information Theory. • For the first time in history, we can use the forces of nature to implement perfectly secure cryptosystems. • It is the science of exploiting the quantum mechanical properties to perform cryptographic tasks. • Its main advantage is that it allows the completion of various cryptographic tasks that are proven or assume to be impossible using only classical communication.
  • 10. History: • Quantum cryptography is based on 2 major elements of quantum mechanics as the base of its implementation. • 1) Heisenberg uncertainty principle: At the instant at which the position of the electron is known, its momentum therefore can be known only up to magnitudes which correspond to that discontinuous change; thus, the more precisely the position is determined, the less precisely the momentum is known, and conversely. • 2)Principle of photon polarization: It is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization or a superposition of two.
  • 11. Another Principle of Quantum Cryptography: • The No Cloning Theorem: It states that it is impossible to create a copy of an arbitrary unknown quantum state. This makes it impossible to perform eavesdropping because it will quickly be detected and thus guarantees that the communicated data remains private.
  • 12. Quantum Key Distribution: • Quantum Key Distribution exploits the effects discussed in order to thwart eavesdropping. • It enables two parties to produce a shared random bit string known only to them, which can be used as a key for encryption and decryption. • If an eavesdropper uses the wrong polarization basis to measure the channel, the result of the measurement will be random.
  • 13. QKD Components: • A fiber or free-space quantum channel to send quantum states of light between the transmitter (Alice) and receiver (Bob). This channel does not need to be secured. • A public but authenticated communication link between the two parties to perform post-processing steps and distill a correct and secret key. • A key exchange protocol that exploits quantum properties to ensure security by detecting eavesdropping or errors, and by calculating the amount of information that has been intercepted or lost. Both errors and potential information leakage are removed during subsequent error correction and privacy amplification post-processing steps, leaving Bob and Alice with a shared key known only to them.
  • 14. Types of Quantum Key Distribution: • 1. Discrete variable QKD: It encodes quantum information in discrete variables and uses single photon detectors to measure the received quantum states. Example: BB84 and E91 protocols. • 2. Contiguous variable QKD: IN this the quantum information is encoded onto the amplitude and phase quadratures of a coherent laser and then can be measured by the receiver using homodyne detectors. • Both these approaches have been proven to be information theoretically secure even in the presence of an attacker or eavesdropper.
  • 15.
  • 16. QKD Protocols: • A protocol is a set of rules governing the exchange of messages over a channel. • A security protocol is a special protocol designed to ensure security properties are met during communications. • There are three main security protocols for QKD: BB84, B92, and Entanglement-Based QKD.
  • 17. BB84 Protocol • BB84 was the first security protocol implementing Quantum 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! • BB84 with no eavesdropping • Bob receives the photons and must decode them using a random basis. • Photon Basis? + + × + × Bit? 0 0 0 1 1 Some of his measurements are correct.
  • 18. Continued: • BB84 with no eavesdropping: • Bob receives the photons and must decode them using a random basis. • In the below figure some of his measurements are correct.
  • 19.
  • 20. • As long as no errors 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.
  • 21. B92 Protocol • Similar to BB84 but uses only 2 out of 4 BB84 state, which makes it easy to implement. • It encodes classical bits in two non orthogonal states. Since no measurement can distinguish two non orthogonal quantum states, it makes it impossible to identify the bit with certainty. • If there is any attempt to learn the bit, it will modify the state in a noticeable way. B92 allows a receiver to learn whenever he gets the bit sent without further discussion with Alice. • In B92, the classical bit b=0 is encoded by a photon with horizontal polarization and b=1 is encoded by photon with polarization angle 45 degrees.
  • 22. Theoretical threats to Quantum cryptography • A hacker can blind a detector with a strong pulse, rendering it unable to see the secret keeping photons. • photons are often generated using a laser tuned to such a low intensity that its producing one single photon at a time. • There is a certain probability that the laser will make a photon encoded with your secret information and then a second photon with that same information. All an intruder has to do is to steal that second photon and could gain access to the data.