Introduction to Quantum Cryptography

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Introduction to Quantum Cryptography

• Nick Papanikolaou
• nikos_at_dcs.warwick.ac.uk

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The Art of Concealment

• To exchange sensitive information, encryption is
  used
• Encryption schemes in use today are under serious
  threat by quantum computers
• The study of Quantum Computing and Quantum
  Information has yielded
• ways of breaking codes
• ways of making better codes

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This Talk

• About Cryptography
• Making Quantum Codes
• Breaking Classical Codes

Announcement Nicks office hours (Rm
327) Tuesdays 3-4pm Thursdays 2-3pm
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Cryptography

• Cryptography is the science of encoding and
  decoding secret messages.
• Most common form Symmetric Cryptography
• Message M, Key K
• Encryption enc(M,K) c
• Decryption M dec(c,K)

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Classical Cryptography 2

• We assume that the key has been already secretly
  shared between sender/receiver.

Sender enc(M,K) c
Receiver M dec(c,K)
Eavesdropper dec(c,???)
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Perfect Cryptosystems

• In order to decipher the message M, the
  eavesdropper needs to know the key K.
• Assuming K is completely secret, a perfect
  cryptosystem can be used.
• Perfect cryptosystem H(CK)H(C)
• Example One-Time Pad
• Use a different key each time, equal in length to
  the message

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Key Distribution

• How do you exchange the key securely in the first
  place?

Sender K
Receiver K
Eavesdropper K
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QKD

• Quantum mechanics gives us a way of ensuring that
  an eavesdropper, if present, is always detected.
• This is called Quantum Key Distribution.
• Main Idea
• Encode each bit of the key as a qubit.

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Photons as Qubits

• A qubit holds a single quantum state.
• Can be in any mixture of basis states.
• The polarization of a single photon can be used
  as a qubit.

Rectilinear Basis ?
or ?
or ?
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The Diagonal Basis

• We can also encode a qubit as a photon in the
  diagonal basis

Diagonal Basis ?
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Quantum Measurement

• Observing a photon changes its state.

Calcite Crystal
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Measurement 2

• If a photon is measured using the wrong
  polarization angle for the crystal, then the
  result will be
• Correct with probability 50
• Incorrect with probability 50
• Therefore, if an eavesdropper made a measurement
  in the wrong basis, his result would be random
  and he would be detected.

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Review of QKD

• The basic idea is that each bit in the key is
  mapped to a photon with a specific polarization.
• e.g. 0 1 0 1 0 1 1
• Bases ? ? ?? ?? ?
• Photons ?? ?? ?? ?

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Eavesdropping

• An eavesdropper can choose a basis for decoding
  at random. For previous example
• Photons received ?? ?? ?? ?
• Bases chosen ?? ?? ???
• Result ? ? 0 1 ? ? ?
• To get all of n bits correctly, probability is
  only 0.5n
• So for 64 bits, eavesdropper only has chance
  5.4?10-20 of getting the right answer.

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Breaking Classical Codes
Peter Shor, ATT Labs If computers that you
build are quantum, Then spies of all factions
will want 'em. Our codes will all fail, And
they'll read our email, Till we've crypto
that's quantum, and daunt 'em.

• Invented a quantum algorithm for efficiently
  finding the prime factors of large numbers.
• Classical factoring algorithms O((log N)k)
• Shors algorithm O(log N)

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Afterword

• Einstein was a giant.
• His head was in the clouds,
• But his feet were on the ground.
• But for those of us who are not that tall,
• We have to choose somewhere inbetween.

- Richard Feynman, on quantum mechanics