Quantum Computation: Is RSA All Factored Out

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Quantum Computation: Is RSA All Factored Out

  1. 1. Quantum ComputationIs RSA All Factored Out?<br />J. Caleb Wherry<br />Austin Peay State University<br />
  2. 2. Outline<br />Introduction to ClassicalComputing<br /><ul><li>Classical Bits & Logic Gates
  3. 3. ComputationalComplexity Classes</li></ul>Introduction to Quantum Computing<br /><ul><li>History
  4. 4. Qubits, Quantum Logic Gates, & BQP Complexity Class
  5. 5. Entanglement, Teleportation, & SuperdenseCoding
  6. 6. Applications of Quantum Computers
  7. 7. ExponentiallyFaster Factoring</li></ul>Future of Quantum Computers<br /><ul><li>Advantages & Disadvantages</li></li></ul><li>Introduction to ClassicalComputing<br />How do classical computers work?<br /><ul><li>Classical Bits:</li></ul> 0 or 1<br />Low Voltage High Voltage<br /><ul><li>UniversalLogic Gates:</li></li></ul><li>Introduction to ClassicalComputing<br />ComputationalComplexity Classes<br />
  8. 8. Introduction to Quantum Computing<br />History<br /><ul><li>Paul Benioff (1980)
  9. 9. Arrays of spins (atoms) couldperformreversablecomputing
  10. 10. Richard Feynman (1982)
  11. 11. Proposed first non-trivial application for quantum computing (simulating quantum systems)
  12. 12. Seth Lloyd (1993)
  13. 13. Showed how quantum computers couldbeconstructed
  14. 14. Peter Shor (1994)
  15. 15. Discovered first « killer app » for quantum computers
  16. 16. Factor numbersexponentiallyfasterthanclassical computers</li></li></ul><li>Introduction to Quantum Computing<br />How do quantum computers work?<br /><ul><li>Quantum Bits (Qubits):</li></ul>|0 or |1<br /> Superposition<br /> |0 + |1<br /><ul><li>Quantum Logic Gates:</li></ul>Allows us to compute 2n bits of information!!! <br />
  17. 17. Introduction to Quantum Computing<br />Entanglement<br /><ul><li>« Spookinessat a distance. » - Einstein
  18. 18. No seen interactions betweenparticles</li></ul>Teleportation<br /><ul><li>Like Star Trek!</li></ul>Superdensecoding<br /><ul><li>Multiple bits of information with one bit </li></li></ul><li>Introduction to Quantum Computing<br />New ComputationalComplexity Classes<br />Image Source: http://en.wikipedia.org/wiki/Quantum_computer<br />
  19. 19. Applications of Quantum Computers<br />Factoring<br /><ul><li>Public-keycryptography (RSA)</li></ul>ClassicalMeans<br /><ul><li>r = m*q wherem,q are prime
  20. 20. Ways to computefactors?
  21. 21. Brute force
  22. 22. GCD
  23. 23. Exponentionally hard</li></li></ul><li>Applications of Quantum Computers<br />Factoring by quantum means:<br /><ul><li>Exponentaillyfasterthanclassical computers
  24. 24. ~O(N2)
  25. 25. Double-slitexperiment
  26. 26. Use of entanglement & destructive interference
  27. 27. Poses a major threat to toclassicalmethods
  28. 28. New types of cryptographycanbeused
  29. 29. Lattice-based</li></li></ul><li>Applications of Quantum Computers<br />UnorderedDatabaseSearching<br /><ul><li>Based on Grover’salgorithm
  30. 30. Probabilisticalgorithm
  31. 31. ~O(√N)</li></ul>Simulating quantum systems<br /><ul><li>Ability to simulate quantum systemsefficiently</li></li></ul><li>Future of Quantum Computers<br />Moore’s Law<br /><ul><li>~10-20 years, currentcomputingwillbe on the nano scale
  32. 32. Quantum forces willbeatwork
  33. 33. New research shows promise
  34. 34. Ability to solvesystems of trillions of equations</li></ul>Advantages<br /><ul><li>Bring about new encryption techniques
  35. 35. Accuratlysimulate quantum systems</li></ul>Disadvantages/Shortcomings<br /><ul><li>Cannot (as of yet) solve NP problems
  36. 36. Extremeenvironmentsneeded to work in</li></li></ul><li>References<br />Bernstein, E., Vazirani, U., « Quantum ComplexityTheory. »<br />Chuang, I., « Quantum Algorithms and theirimplementations: QuISU – An Introduction for Undergraduates. »<br />Lloyd, S., « Quantum Information Science. »<br />Nielson, M., Chuang, I., « Quantum Computation and Quantum Information. »<br />
  37. 37. SpecialThanks<br />MIT QuISU<br />Quantum Information Science for Undergraduates<br />http://www.rle.mit.edu/quisu<br />
  38. 38. Questions?<br />Comments?<br />

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