Independence of Tabulation-Based Hash Classes

Approximately Minwise Independence with Twisted Tabulation

A random hash function h is ε-minwise if for any set S, |S| “ n, and element x P S, Prrhpxq “ minhpSqs “ p1 ̆ εq{n. Minwise hash functions with low bias ε have widespread applications within similarity estimation. Hashing from a universe rus, the twisted tabulation hashing of Pǎtraşcu and Thorup [SODA’13] makes c “ Op1q lookups in tables of size u1{c. Twisted tabulation was invented to get good ...

An Improved Hash Function Based on the Tillich-Zémor Hash Function

Using the idea behind the Tillich-Zémor hash function, we propose a new hash function. Our hash function is parallelizable and its collision resistance is implied by a hardness assumption on a mathematical problem. Also, it is secure against the known attacks. It is the most secure variant of the Tillich-Zémor hash function until now.

Appendix for Tabulation Based 4-Universal Hashing with Applications to Second Moment Estimation

Practical Hash Functions for Similarity Estimation and Dimensionality Reduction

Hashing is a basic tool for dimensionality reduction employed in several aspects of machine learning. However, the perfomance analysis is often carried out under the abstract assumption that a truly random unit cost hash function is used, without concern for which concrete hash function is employed. The concrete hash function may work fine on sufficiently random input. The question is if they c...

Lecture 10 — March 20 , 2012

In the last lecture, we finished up talking about memory hierarchies and linked cache-oblivious data structures with geometric data structures. In this lecture we talk about different approaches to hashing. First, we talk about different hash functions and their properties, from basic universality to k-wise independence to a simple but effective hash function called simple tabulation. Then, we ...