This document summarizes Rusins Frievald's algorithm for matrix product verification. It discusses how the algorithm works by analyzing the error probability and techniques for reducing it. It also mentions other applications of the algorithm in areas like cryptography and fingerprinting techniques.

1. Randomized Algorithms
CS648
Lecture 5
• Algebraic Techniques
• Frievald’s Algorithm
• Fingerprinting Techniques
1

2. FRIEVALD’S TECHNIQUE
APPLICATION
MATRIX PRODUCT VERIFICATION
2

3. Frievald’s Algorithm
(Rusins Frievald, 1977)
3

4. Frievald’s Algorithm
(Rusins Frievald, 1977)
4

5. Frievald’s Algorithm
(Rusins Frievald, 1977)
5

6. Frievald’s Algorithm
(Analyzing error probability)
6
null vector

7. Frievald’s Algorithm
(Analyzing error probability)
7

8. Frievald’s Algorithm
(Analyzing error probability)
8

9. Probability tool:
Partition of sample space
9
Ω

10. Question: When to use the Partition theorem ?
10

11. Frievald’s Algorithm
(Analyzing error probability)
11

12. Frievald’s Algorithm
(Analyzing error probability)
12
≠0
Could be 0, 1 or some other number

13. Frievald’s Algorithm
(Analyzing error probability)
13

14. Frievald’s Algorithm
(reducing the error probability)
14

15. Frievald’s Algorithm
(final result)
15

16. FINGERPRINTING
APPLICATION
CRYPTOGRAPHY
16

17. PRIME NUMBERS
(SOME BASIC FACTS)
17

18. 18
100 25
1000 168
10000 1229
100000 9592
1000000 78498

19. 19

20. 20

21. 21
Aim: To determine if File A identical to File B by communicating fewest bits ?
File A File B

22. Question: What is a File ?
Answer:
A bit string.
22

23. Visualize a file as a binary number
23

24. 24

25. RandomEqualityChecking-Protocol
(bounding the error probability)
25

26. RandomEqualityChecking-Protocol
(bounding the error probability)
26

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