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Lecture 5-cs648

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Lecture 5-cs648

  1. 1. Randomized Algorithms CS648 Lecture 5 • Algebraic Techniques • Frievald’s Algorithm • Fingerprinting Techniques 1
  2. 2. FRIEVALD’S TECHNIQUE APPLICATION MATRIX PRODUCT VERIFICATION 2
  3. 3. Frievald’s Algorithm (Rusins Frievald, 1977) 3
  4. 4. Frievald’s Algorithm (Rusins Frievald, 1977) 4
  5. 5. Frievald’s Algorithm (Rusins Frievald, 1977) 5
  6. 6. Frievald’s Algorithm (Analyzing error probability) null vector 6
  7. 7. Frievald’s Algorithm (Analyzing error probability) 7
  8. 8. Frievald’s Algorithm (Analyzing error probability) 8
  9. 9. Probability tool: Partition of sample space Ω 9
  10. 10. Question: When to use the Partition theorem ? 10
  11. 11. Frievald’s Algorithm (Analyzing error probability) 11
  12. 12. Frievald’s Algorithm (Analyzing error probability) ≠0 Could be 0, 1 or some other number 12
  13. 13. Frievald’s Algorithm (Analyzing error probability) 13
  14. 14. Frievald’s Algorithm (reducing the error probability) 14
  15. 15. Frievald’s Algorithm (final result) 15
  16. 16. FINGERPRINTING APPLICATION CRYPTOGRAPHY 16
  17. 17. PRIME NUMBERS (SOME BASIC FACTS) 17
  18. 18. 100 25 1000 168 10000 1229 100000 9592 1000000 78498 18
  19. 19. 19
  20. 20. 20
  21. 21. File A File B Aim: To determine if File A identical to File B by communicating fewest bits ? 21
  22. 22. Question: What is a File ? Answer: A bit string. 22
  23. 23. Visualize a file as a binary number 23
  24. 24. 24
  25. 25. RandomEqualityChecking-Protocol (bounding the error probability) 25
  26. 26. RandomEqualityChecking-Protocol (bounding the error probability) 26
  27. 27. • Please go through the slides of this lecture carefully and patiently. You are welcome to discuss any doubt in the next class (Saturday, 17th August) 27

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