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Randomized AlgorithmsCS648
Lecture 5
• Algebraic Techniques• Frievald’s Algorithm
• Fingerprinting Techniques
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FRIEVALD’S TECHNIQUEAPPLICATION
MATRIX PRODUCT VERIFICATION
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Frievald’s Algorithm(Rusins Frievald, 1977)
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Frievald’s Algorithm(Rusins Frievald, 1977)
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Frievald’s Algorithm(Rusins Frievald, 1977)
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Frievald’s Algorithm(Analyzing error probability)
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null vector
Frievald’s Algorithm(Analyzing error probability)
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Frievald’s Algorithm(Analyzing error probability)
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Probability tool:Partition of sample space
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Ω
Question: When to use the Partition theorem ?
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Frievald’s Algorithm(Analyzing error probability)
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Frievald’s Algorithm(Analyzing error probability)
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≠0
Could be 0, 1 or some other number
Frievald’s Algorithm(Analyzing error probability)
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Frievald’s Algorithm(reducing the error probability)
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Frievald’s Algorithm (final result)
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FINGERPRINTINGAPPLICATION
CRYPTOGRAPHY
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PRIME NUMBERS(SOME BASIC FACTS)
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100 25
1000 168
10000 1229
100000 9592
1000000 78498
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Aim: To determine if File A identical to File B by communicating fewest bits ?
File A File B
Question: What is a File ?
Answer:
A bit string.
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Visualize a file as a binary number
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RandomEqualityChecking-Protocol(bounding the error probability)
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RandomEqualityChecking-Protocol(bounding the error probability)
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• 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)
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