Lecture 5-cs648

Randomized AlgorithmsCS648

Lecture 5

• Algebraic Techniques• Frievald’s Algorithm

• Fingerprinting Techniques

1

FRIEVALD’S TECHNIQUEAPPLICATION

MATRIX PRODUCT VERIFICATION

2

Frievald’s Algorithm(Rusins Frievald, 1977)

3

Frievald’s Algorithm(Rusins Frievald, 1977)

4

Frievald’s Algorithm(Rusins Frievald, 1977)

5

Frievald’s Algorithm(Analyzing error probability)

6

null vector

Frievald’s Algorithm(Analyzing error probability)

7

Frievald’s Algorithm(Analyzing error probability)

8

Probability tool:Partition of sample space

9

Ω

Question: When to use the Partition theorem ?

10

Frievald’s Algorithm(Analyzing error probability)

11

Frievald’s Algorithm(Analyzing error probability)

12

≠0

Could be 0, 1 or some other number

Frievald’s Algorithm(Analyzing error probability)

13

Frievald’s Algorithm(reducing the error probability)

14

Frievald’s Algorithm (final result)

15

FINGERPRINTINGAPPLICATION

CRYPTOGRAPHY

16

PRIME NUMBERS(SOME BASIC FACTS)

17

18

100 25

1000 168

10000 1229

100000 9592

1000000 78498

19

20

21

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.

22

Visualize a file as a binary number

23

24

RandomEqualityChecking-Protocol(bounding the error probability)

25

RandomEqualityChecking-Protocol(bounding the error probability)

26

• 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