Combinatorics on words in information security: Unavoidable regularities in the construction of multicollision attacks on iterated hash functions

TL;DR

This paper explores combinatorial properties of constrained long words and their implications for multicollision attacks on generalized iterated hash functions, revealing unavoidable regularities that can be exploited in cryptanalysis.

Contribution

It introduces a novel combinatorial framework for analyzing long words with symbol occurrence restrictions and links these properties to vulnerabilities in hash function security.

Findings

Identifies unavoidable regularities in constrained long words.

Connects combinatorial properties to multicollision attack strategies.

Provides insights into hash function security vulnerabilities.

Abstract

Classically in combinatorics on words one studies unavoidable regularities that appear in sufficiently long strings of symbols over a fixed size alphabet. In this paper we take another viewpoint and focus on combinatorial properties of long words in which the number of occurrences of any symbol is restritced by a fixed constant. We then demonstrate the connection of these properties to constructing multicollision attacks on so called generalized iterated hash functions.