QUANTUM CRYPTOGRAPHY

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QUANTUM CRYPTOGRAPHY
Security through Uncertainty
CS 265 Spring 2003

• Narayana D Kashyap

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Classic Cryptography

• Keys by Transposition and Substitution
• Strength mainly on Long Keys
• KDC
• Mathematical Concepts
• Allows the eavesdropper in principle to measure
  physical properties without disturbing them.

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Quantum vs. Classic

• Physics instead of Math
• Exchange of information very secure in a strong
  sense.
• Laws of physics guarantee (probabilistically)
  that the secret key exchange will be secure.
• The ACT OF MEASUREMENT is an integral part of
  quantum mechanics, not just a passive, external
  process as in Classic Crypto.

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Fundamental Concepts

• Quantum Channel along with Quantum theory
• Heisenberg Uncertainty Principle
• certain pairs of physical properties are
  complementary.
• Any effort to monitor the channel necessarily
  disturbs the signal in some detectable way.
• The uncertainty principle is used to build secure
  channel based on Quantum properties of light.
• Photons Polarization

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How it works?

• Bob, informed about polarization being either 0
  or 90 (rectilinear), can find out by his
  photomultiplier as to how it was sent.
• Such an apparatus is useless for distinguishing
  45 or 135 (diagonal) photons - unless the
  apparatus is turned 45 degrees.
• Rectilinear and Diagonal polarizations are
  complementary properties.

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BB84

• Bennett and Brassard proposed in 1984
• Quantum channel Polarized Photons
• Public channel Normal Messages
• Alice Sender Bob receiver
• Agreed before hand that
• 90 and 45 are 1s
• 0 and 135 are 0s

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Quantum Key Distribution
Alice
Bob
Alice
? ? ? ?
?
Bob
1 1 0 0
1
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Verification of QC

• Alice and Bob to compare the "parity"-evenness or
  oddness of a publicly agreed on random subset
  containing about half the bits in their data.
• Alice could tell Bob, "I looked at the 1st, 3rd,
  4th, 9th,...996th and 999th of my 1,000 bits of
  data, and they include an even number of l's."
• It suffices to repeat the test 20 times, with 20
  different random subsets, to reduce the chance of
  an undetected error to less than one in a
  million.

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References

• Quantum Cryptography
• http//www.cyberbeach.net/jdwyer/quantum_crypto/
  quantum1.htm
• Quantum Cryptography Tutorial
• http//www.cs.dartmouth.edu/jford/crypto.html
• Oxford Quantum Computation Group
• http//www.qubit.org/