Quantum Cryptography

1
Quantum Cryptography

• Alex Chen

2
Outline

• Classical Cryptography
• Quantum Mechanics
• Quantum Cryptography
• Summary

3
Classical Cryptography

• Potential Weaknesses in Todays Keys
• RSA Securitys RC5-64 algorithm broken
• A student at Notre Dame University, using 10,000
  computers working around the clock for 549 days,
  broke 109-bit key.
• Advancement of Mathematics
• A computer scientist named Manindra Agrawal
  recently solved the problem that has baffled
  scientists for centuries how to tell if a number
  is prime without performing any factoring may
  open the door to figure out how to factor large
  numbers.

4
Classical Cryptography

• Advancement in computer hardware
• Peter Shor of ATT Laboratories invented quantum
  algorithm to quickly factor large numbers
  reduce order of magnitude time spent to factor a
  large number.

5
Quantum Mechanics

• Heisenberg Uncertainty Principle
• If you measure one thing, you cannot measure
  another thing accurately. E.g. You can measure a
  persons height, but not his weight accurately,
  and vice versa.
• Until the point of measurement, the object exist
  in an indeterminate or fuzzy state.
• Extend through time and space
• If a physical process creates a pair of photons,
  and this pair of photons travels in opposite
  directions at the speed of light for millions of
  years, a strange thing happens if one of the
  photons is examined by a human observer if the
  polarity of the observed photon is vertical, the
  polarization of the photon that is millions of
  light years away, at the same instant, becomes
  horizontal.

6
Quantum Mechanics

• Act of measurement will actually cause the other
  photon to commit to a certain state.
• Some scientists believe it will be possible to
  teleport matter using quantum properties.
• In practice, these principles have been applied
  to photons.
• Not possible to tamper with messages sent using
  photons without changing the properties of the
  message.
• Ideal for key distribution.

7
Quantum Cryptography

• Secure for 3 reasons
• No-cloning theorem states that an unknown quantum
  state cannot be cloned.
• In a quantum system, which can be in one of two
  states, any attempt to measure the quantum state
  will disturb the system.
• The effects produced by measuring a quantum
  property is irreversible, which means an
  eavesdropper cannot put back a quantum message to
  its original state.

8
Quantum Cryptography

• Quantum properties of light exploited
• Light has wavelike properties, which can be
  aligned, or polarized, in any direction.
• Sunlight consists of varying wavelengths of light
  polarized in a random fashion.
• Laser light consist of a single wavelength
  polarized in one direction can be used to
  produce photons with given polarization.

9
Quantum Cryptography

• In practice, photons polarized
• Vertically
• Horizontally
• 45 degrees /
• 135 degrees \
• Calcite crystal used as quantum filter.
• If crystal is held in vertical position, photons
  that are vertically or horizontally polarized
  will pass through filter unchanged.

10
Quantum Cryptography

• If a photon that is diagonally polarized passes
  through the vertical filer, polarization will be
  changed to vertical or horizontal in a totally
  random fashion information is lost.
• If eavesdropper reads the message and then
  passes the message to intended recipient, it is
  easy to detect that an unauthorized person read
  the message because original information and
  received information will no longer agree.

11
Quantum Cryptography

• Bennet and Brassard propose how polarized photons
  can be used to distribute keys
• Alice encodes the key using photon polarization
  to denote ones and zeroes. It is important to
  note that Alice will use the and /
  polarizations randomly to encode the zeroes and
  and \ polarizations to encode the ones.
  E.g. 01 can be encode as , \, / ,
  or / \.

12
Quantum Cryptography

• Alice sends the message with the binary string
  100100011 using the following polarizations

13
Quantum Cryptography

• For each photon Alice sends, Bob chooses at
  random a measurement type either the crystal
  vertical or slanted.
• Vertical crystal, which will correctly pass the
  vertical or horizontally polarized photons, is
  also known as a rectilinear measurement and
  denoted as .
• Slanted crystal, which will correctly pass the
  corresponding angled photons, is also known as a
  diagonal measurement and denoted x.
• Bob uses the following random measurements

14
Quantum Cryptography

• In the first measurement above, Bob makes the
  correct measurement and the photon will come
  through the crystal unchanged.
• In the second measurement above, Bob makes the
  wrong measurement and the 45 degree photon will
  come through the crystal as either a horizontal
  or vertical photon information is irretrievably
  lost.
• The following shows the result of Bobs
  measurements

15
Quantum Cryptography

• Bob publicly tells Alice which measurements he
  made (not the results of the measurements).
• Alice publicly tells Bob for which photons he
  made the correct type of measurements.
• The correct measurements made by Bob are checked
  below

16
Quantum Cryptography

• Bob keeps all of the results for which he has
  made the correct measurement and discards the
  rest. The remaining ones and zeroes will make up
  the key as seen in the following diagram.

17
Quantum Cryptography

• Alice and Bob can test for eavesdropping by
  selecting a random subset of results and
  comparing them can be done publicly because
  this subset will not be used for the public key.
• If Eve has intercepted the message, by the rules
  of probability she will have made the wrong
  measurement about half the time, and the photons
  she sends to Bob will have a good probability of
  being wrong.

18
Quantum Cryptography

• What causes errors besides eavesdropping?
• Transmitting and receiving equipment
• Transmission medium air or optical fiber
• Solutions
• To prevent splitting of light waves, very low
  levels are used to transmit data as low as 1/10
  of a photon per transmitted bit.
• Separate errors introduced by eavesdropping from
  errors produced by other things using statistical
  methods called privacy amplification.
• Advantage of privacy amplification over existing
  public keys is that probability of information
  leakage can be proved to be at a certain level
  while public keys have never been proven secure
  just widely believed that no one has learned how
  to factor large prime numbers yet.

19
Summary

• Still a new field, but holds much potential and
  practical applications.
• May revolutionize the way we do secure
  communication in the future.
• May satisfy the encryption needs of users,
  perhaps indefinitely.

20
References

• Nicolas Gisin, Gregoire Ribordy, Wolfgang Tittel,
  and Hugo Abinden, Quantum Cryptography, Reviews
  of Modern Physics, 2002
• Samuel Lomonaco, A Quick Glance at Quantum
  Cryptography, 1998
• Hoi-Kwong Lo, Quantum Cryptography,
  Hewlett-Packard Labs, 1997