The universality of iterated hashing over variable-length strings

TL;DR

This paper investigates the properties of iterated hash functions, proving their limitations in independence and establishing bounds on their universality over long strings, which informs their applicability in various hashing scenarios.

Contribution

It provides theoretical proofs of the independence limitations of iterated hashing and bounds on their universality for long strings, advancing understanding of their theoretical capabilities.

Findings

Iterated hash functions can be pairwise independent.

They cannot achieve 3-wise independence.

Bounds are established for their universality over long strings.

Abstract

Iterated hash functions process strings recursively, one character at a time. At each iteration, they compute a new hash value from the preceding hash value and the next character. We prove that iterated hashing can be pairwise independent, but never 3-wise independent. We show that it can be almost universal over strings much longer than the number of hash values; we bound the maximal string length given the collision probability.