1. Hashing
Project by: Omar Benismail
Comp3801

2. In this presentation: What is hashing?
Types of hashing that I covered.
Secure hashing.
Min-Hashing.
Best hashing algorithm.

3. A hash function is any function that can be used to map data of arbitrary size to data of fixed size.

4. A good hash function will arbitrarily map a value to a hash code with equal probability.
One common problem is when our universe far exceeds the size of our hashing codes (PHP)

5. What happened since the last presentation?

6. Types of hashing that I covered
Secure hashing
Min-Hashing

7. Secure Hashing
SHA -series
MDS -series

8. Secure Hashing (cont.) Speed isn’t an issue
Could have really complex algos.
Hash codes have a larger size

9. Secure Hashing (cont. 2)

11. SHA-1 and MDS-5 http://www.miraclesalad.com/webtools/md5.php

12. Min-Hashing Hashes in constant time
Hash codes are usually small numbers
Usually converts the keys to natural numbers (for speed)
Sometimes implies a hash-table

13. Min-Hashing & Hash-tables
For m = size of table
For k = key entered

14. Simple algorithms
Division method
H(k)= k mod m
If m = 2 𝑝 bad

15. Simple algorithms Division method H(k)= k mod m If m = 2 𝑝 -1 better
multiplication method
H(k)= m(kA mod 1)

16. Universal hashing
Uses random hash functions that are independent of the key inputted
We set p to a large prime number.

17. Universal hashing ha,b (k) = ((a*k + b) mod p) mod m
h(k) = ((a*k)mod 2 𝑤 ) div 2 𝑤−𝑑

18. Dealing with collisions
chaining
Θ(1 + α)

19. Dealing with collisions
Linear probing
One problem is resizing

20. Perfect hashing

21. Best hashing algorithm is….
Depends

22. Questions
What is the main difference between secure hashing and minHashing / universalHashing?
What type of mapping function (secure or universal) would you use for these tasks:
Converting a password to a hash-code
For storing items in a hash-table
Implementing bloom’s filter
Implementing a cryptographic hashing algorithm
3. Describe one example from class where hashing was used.
4. Describe one of the hash table implantations that deals with collisions.
5. That is the main constraint for a perfect hashing algorithm to work?
6. From the slides What do the values a, b and m represent?